Put options are contracts to sell. You pay me a fee for the right to put the stock (or other underlying security) in my hands if you want to. That happens on a specific date (the strike date) and a specified price (the strike price). You can decide not to exercise that right, but I must follow through and let you sell it to me if you want to. Put options can be used by the purchaser to cap losses.

For example: You purchase a PUT option for GE Oct19 13.00 from me. On October 19th, you can make me buy your GE stock for $13.00 a share. If the price for GE has fallen to $12.00, that would be a good idea. If its now at $15.00 a share, you will probably keep the GE or sell it at the current market price.

Call options are contracts to buy. The same idea only in the other direction: You pay me a fee for the right to call the stock away from me. Calls also have a strike date and strike price. Like a put, you can choose not to exercises it. You can choose to buy the stock from me (on the strike date for the strike price), and I have to sell it to you if you want it.

For example: You purchase a CALL option for GE Oct19 16.00 from me. On October 19th, you can buy my GE stock for $16.00 a share. If the current price is $17.50, you should make me sell it to you for $16.00. If its less than $16.00, you could by it at the current market price for less.

Commonly, options are for a block of 100 shares of the underlying security.

Note: this is a general description. Options can be very complicated. The fee you pay for the option and the transaction fees associated with the shares affects whether or not exercising is financially beneficial. Options can be VERY RISKY. You can loose all your money as there is no innate value in the option, only how it relates to the underlying security. Before your brokerage will let you trade, there are disclosures you must read and affirm that you understand the risk.

I'm normally a fan of trying to put all the relevant info in an answer when possible, but this one's tough to do in one page. Here's the best way, by far to learn the basics:

The OIC (Options Industry Council) has a great, free website to teach investors at all levels about options.

You can set up a learning path that will remember which lessons you've done, etc. And they're really, truly not trying to sell you anything; their purpose is to promote the understanding and use of options.

A 'Call' gives you the right, but not the obligation, to buy a stock at a particular price. The price, called the "strike price" is fixed when you buy the option. Let's run through an example -

AAPL trades @ $259. You think it's going up over the next year, and you decide to buy the $280 Jan11 call for $12.

Here are the details of this trade. Your cost is $1200 as options are traded on 100 shares each. You start to have the potential to make money only as Apple rises above $280 and the option trades "in the money." It would take a move to $292 for you to break even, but after that, you are making $100 for each dollar it goes higher. At $300, your $1200 would be worth $2000, for example. A 16% move on the stock and a 67% increase on your money. On the other hand, if the stock doesn't rise enough by January 2011, you lose it all.

A couple points here - American options are traded at any time. If the stock goes up next week, your $1200 may be worth $1500 and you can sell. If the option is not "in the money" its value is pure time value. There have been claims made that most options expire worthless. This of course is nonsense, you can see there will always be options with a strike below the price of the stock at expiration and those options are "in the money." Of course, we don't know what those options were traded at.

On the other end of this trade is the option seller. If he owns Apple, the sale is called a "covered call" and he is basically saying he's ok if the stock goes up enough that the buyer will get his shares for that price. For him, he knows that he'll get $292 (the $280, plus the option sale of $12) for a stock that is only $259 today. If the stock stays under $280, he just pocketed $12, 4.6% of the stock value, in just 3 months. This is why call writing can be a decent strategy for some investors. Especially if the market goes down, you can think of it as the investor lowering his cost by that $12. This particular strategy works best in a flat to down market. Of course in a fast rising market, the seller misses out on potentially high gains.

(I'll call it quits here, just to say a Put is the mirror image, you have the right to sell a stock at a given price. It's the difference similar to shorting a stock as opposed to buying it.)

If you have a follow up question - happy to help.

EDIT - Apple closed on Jan 21, 2011 at $326.72, the $280 call would have been worth $46.72 vs the purchase price of $12. Nearly 4X return (A 289% gain) in just over 4 months for a stock move of 26%. This is the leverage you can have with options. Any stock could just as easily trade flat to down, and the entire option premium, lost.

"Put DOWN"

(buy these when you expect the price to go down)

How it works

You 'lock in' the price you can sell at.

If the price goes down below the 'locked-in' price, you buy at the new low price and sell at the higher 'locked-in' price; make money.

"Call UP"

(buy these when you expect the price to go up)

How it works

You 'lock in' the price you can buy at.

If the price goes up above the 'locked-in' price, you buy at the 'locked-in' price and sell at the new higher price, make money.

In either case

1. You pay a small fee to 'lock in' the price
2. You don't have to do anything if the price doesn't change to make it profitable for you. It's optional, which is why it's called an "option".

An Xbox currently sells for $200 but you don't have the money right now to buy it. You think the price of the xbox is going up to $250 next month. Your friend works at BestBuy and says he has a "raincheck" that allows you to buy the Xbox for $200 but the raincheck expires next month. He offers to sell you the "raincheck" for $5.

When you buy his raincheck for $5 you are locking in the right to buy the Xbox for $200. It is like an option because it locks in the purchase price, it has an expiration date, it locks in a purchase price, and it is not mandatory that you redeem it.

That's an explanation for a call option in kids terms. For more easy answers to the question what is a call option click now.

A put can be answered in a similar way. Suppose you bought the Xbox for $250 and then the price drops back to $200. If you keep your receipt, you have the right to return (sell the Xbox back) for $250 even though the current price is only $200. Bestbuy has a 30 day return policy so your receipt is like a put option in that you can sell the Xbox back for a price higher than the current market price.

That's a simple example of a put option in kids terms. For more easy answers to the question what is a put click now.

Great answer by @duffbeer. Only thing to add is that the option itself becomes a tradeable asset. Here's my go at filling out the answer from @duffbeer.

"Hey kid... So you have this brand-new video game Manic Mazes that you paid $50 for on Jan 1st that you want to sell two months from now"

"Yes, Mr. Video Game Broker, but I want to lock in a price so I know how much to save for a new Tickle Me Elmo for my baby sister."

"Ok, for $3, I'll sell you a 'Put' option so you can sell the game to me for $40 in two months."

Kid says "Ok!", sends $3 to Mr Game Broker who sends our kid a piece of paper saying:

The holder of this piece of paper can sell the game Manic Mazes to Mr Game Broker for $40 on March 1st.

.... One month later ....

News comes out that Manic Mazes is full of bugs, and the price in the shops is heavily discounted to $30.

Mr Options Trader realizes that our kid holds a contract written by Mr Game Broker which effectively allows our kid to sell the game at $10 over the price of the new game, so maybe about $15 over the price in the second-hand market (which he reckons might be about $25 on March 1st). He calls up our kid.

"Hey kid, you know that Put option that Mr Game Broker sold to you you a month ago, wanna sell it to me for $13?" (He wants to get it a couple of bucks cheaper than his $15 fair valuation.)

Kid thinks:

hmmm ... that would be a $10 net profit for me on that Put Option, but I wouldn't be able to sell the game for $40 next month, I'd likely only get something like $25 for it.

So I would kind-of be getting $10 now rather than potentially getting $12 in a month.

Note: The $12 is because there could be $15 from exercising the put option (selling for $40 a game worth only $25 in the second-hand market) minus the original cost of $3 for the Put option.

Kid likes the idea and replies:

"Done!".

Next day kid sends the Put option contract to Mr Options Trader and receives $13 in return.

In summary

Our kid bought the Put option and later sold it for a profit, and all of this happened before the option reached its expiry date.

In addition to all these great answers, check out the Wikipedia entry on options.

The most important thing to note from their definition is that an option is a derivative (and nothing about any derivative is simple). Because it is a derivative, increases or decreases in the price of the underlying stock won't automatically result in the same amount of change in the value of the option.

So, child, your goal is to make money? This is usually achieved by selling goods (say, lemonade) at a price that exceeds their cost (say, sugar, water and, well, lemons).

Options, at first, are very much same in that you can buy the right to engage in a specific future trade. You make money in this situation if the eventual returns from the scheduled trade cover the cost of purchasing the option. Otherwise you can simply opt out of the trade -- you purchased the right to trade, after all, not any type of obligation. Makes sense? Good. Because what follows is what makes options a little different.

That is, if you sell that same right to engage in a specific trade the situation is seemingly reversed: you lock in your return at the outset, but the costs aren't fully realized until the trade is either consumed or declined by the owner of the option. And keep in mind that it is always the owner of the option who is in the driver's seat; they may sell the option, hold on to it and do nothing, or use it to engage in the anticipated trade. And that's really all there's to it.

Put Options for Kids:

You have a big box of candy bars. You saved up your allowance to get a lot of them, so you could have one whenever you want one. But, you just saw a commercial on TV for a new toy coming out in one month. Your allowance alone won't buy it, and you want that toy more than you want the candy. So, you decide that you'll sell the candy to your friends at school to buy the toy.

Now, you have a choice. You can sell the candy now, and put the money in your piggy bank to buy the toy later. Or, you can save the candy, and sell it in a month when you actually need the money to buy the toy. You know that if you sell all the candy you have today, you can get 50 cents a bar. That's not quite enough to buy the toy, but your allowance will cover the rest.

What you don't know is how much you might be able to sell the candy for in a month. You might be able to get 75 cents a bar. If you did, you could pay for the toy with just the money from the candy and even have some left over. But, you might only be able to sell them for 25 cents each, and you wouldn't have enough to buy the toy even with your allowance. You'd like to wait and see if you could get 75 cents each, but you don't want to risk getting only 25 cents each.

So, you go to your father. He and his co-workers like these candy bars too, so he'd be willing to buy them all and sell them to his friends the way you're planning to do with yours. You ask for the option to sell him all the candy bars for 50 cents each in one month. If you find out you can get more for them at school, you want to be able to take that deal, but if you can't sell them for 50 cents at school, you'll sell them to your dad.

Now, your dad knows that he could have the same problem selling the candy at 50 cents or more that you are afraid of. So, he offers a compromise. If you pay him $5 now, he'll agree to the deal. You figure that even without that $5, between your allowance and the candy money, you can still buy the toy. So, you take the deal.

In one month, you can offer the candy at school. If nobody will pay 50 cents, you can sell the candy to your dad when you get home, but if the kids at school will pay 50 cents or more, you can sell it all at school. Either way, you have enough money to buy the toy, and you can also choose which price to accept, but you had to pay your dad $5, and you can't get that back, so if it turns out that you can sell the candy at school for 50 cents, same as today, then because you paid the $5 you don't end up with as much as if you'd simply waited.

In the financial market, this type of option is a "put option". Someone who owns something that's traded on the market, like a stock, can arrange to sell that stock to someone else at an agreed-on price, and the seller can additionally pay some money to the buyer up front for the option to not sell at that price. Now, if the stock market goes up, the seller lets the contract expire and sells his stock on the open market. If it goes down, he can exercise the option, and sell at the agreed-upon price to the buyer. If, however, the stock stays about the same, whether he chooses to sell or not, the money the seller paid for the option means he ends up with less than he would have if he hadn't bought the option.

Call Options for Kids:

Let's say that you see another ad on TV for another toy that you like, that was just released. You check the suggested retail price on the company's web site, and you see that if you save your allowance for the next month, you can buy it.

But, in school the next day, everybody's talking about this toy, saying how they want one. Some already have enough money, others are saving up and will be able to get it before you can. You're afraid that because everyone else wants one, it'll drive up the price for them at the local store, so that your month's allowance will no longer buy the toy.

So, you go to your dad again. You want to be able to use your allowance money for the next month to buy the new toy. You're willing to wait until you actually have the money saved up before you get the toy, but you need that toy in a month. So, you want your dad to buy one for you, and hold it until you can save up to buy it from him. But, you still want it both ways; if the price goes down in a month because the toy's not so new anymore and people don't want it, you don't want to spend your entire month's allowance buying the one from your dad; you just want to go to the store and buy one at the lower price. You'll pay him $5 for the trouble, right now, whether you buy the toy he got you or not.

Your dad doesn't want to have a toy he's not using sitting around for a month, especially if you might not end up buying it from him, so he offers a different deal; In one month, if you still want it, he'll stop by the store on his way home and pick up the toy. You'll then reimburse him from the allowance you saved up; if it ends up costing less than a month's allowance, so be it, but if it costs more than that, you won't have to pay any more. This will only cost you $3, because it's easier for him. But, because he's not buying it now, there is a small chance that the item will be out of stock when he goes to buy it, and you'll have to wait until it's back in stock. You agree, on the condition that if you have to wait longer than a month for your toy, because he couldn't get one to sell you, he pays you back your $3 and knocks another $5 off the cost to buy the toy from him.

The basic deal to buy something at an agreed price, with the option not to do so, is known as a "call option". Someone who wishes to buy some stocks, bonds or commodities at a future date can arrange a deal with someone who has what they want to buy them at a specific price. The buyer can then pay the seller for the option to not buy.

The counter-offer Dad made, where he will buy the toy from the store at whatever price he can find it, then sell it to you for the agreed price, is known as a "naked call" in finance. It simply means that the seller, who is in this case offering the option to the buyer, doesn't actually have what they are agreeing to sell at the future date, and would have to buy it on the open market in order to turn around and sell it. This is typically done when the seller is confident that the price will go down, or won't go up by much, between now and the date of the contract. In those cases, either the buyer won't exercise the option and will just buy what they want on the open market, or they'll exercise the option, but the difference between what the seller is paying to buy the commodity on the market and what he's getting by selling it on contract is within the price he received for the option itself. If, however, the price of an item skyrockets, the seller now has to take a significant, real loss of money by buying something and then selling it for far less than he paid. If the item flat-out isn't available, the buyer is usually entitled to penalties for the seller's failure to deliver. If this is all understood by both parties, it can be thought of as a form of insurance.