What is the meaning of "short selling" or "going short" a stock?

Rich's answer captures the basic essence of short selling with example.

I'd like to add these additional points:

• You typically need a specially-privileged brokerage account to perform short selling. If you didn't request short selling when you opened your account, odds are good you don't have it, and that's good because it's not something most people should ever consider doing. Short selling is an advanced trading strategy. Be sure you truly grok selling short before doing it.

• Consider that when buying stock (a.k.a. going long or taking a long position, in contrast to short) then your potential loss as a buyer is limited (i.e. stock goes to zero) and your potential gain unlimited (stock keeps going up, if you're lucky!)

  Whereas, with short selling, it's reversed: Your loss can be unlimited (stock keeps going up, if you're unlucky!) and your potential gain is limited (i.e. stock goes to zero.)

• The proceeds you receive from a short sale – and then some – need to stay in your account to offset the short position. Brokers require this. Typically, margin equivalent to 150% the market value of the shares sold short must be maintained in the account while the short position is open.

• The owner of the borrowed shares is still expecting his dividends, if any. You are responsible for covering the cost of those dividends out of your own pocket.

• To close or cover your short position, you initiate a buy to cover. This is simply a buy order with the intention that it will close out your matching short position.

• You may be forced to cover your short position before you want to and when it is to your disadvantage! Even if you have sufficient margin available to cover your short, there are cases when lenders need their shares back. If too many short sellers are forced to close out positions at the same time, they push up demand for the stock, increasing price and deepening their losses. When this happens, it's called a short squeeze.

• In the eyes of the public who mostly go long buying stock, short sellers are often reviled. However, some people and many short sellers believe they are providing balance to the market and preventing it sometimes from getting ahead of itself.

• [Disambiguation: A short sale in the stock market is not related to the real estate concept of a short sale, which is when a property owner sells his property for less than he owes the bank.]

Additional references:

• Short (finance) at Wikipedia
• Short Selling: What Is Short Selling? at Investopedia

The reason for selling a stock "short" is for when you believe the stock's price will decrease in the near future.

Here is an example: Today Exxon Mobil stock is selling for $100 per share. You expect the price to decrease so you want to short the stock. Your broker borrows the shares from someone who owns them (in house or from another brokerage firm) which are then transferred into your account. You then sell them and receive the proceeds from the sale. Since you borrowed the shares, you will need to return them to the lender at some time in the future.

Let's say you borrow 10 shares @ $100 and you sell them at the market price of $100. You'll receive $1,000 in your account. A few days later, the share price has decreased to $80. Now you can buy 10 shares from the market at a total cost of $800 and you return those shares to the lender. Since you originally took in $1,000 and you just paid out $800, you have a profit of $200.

The 'normal' series of events when trading a stock is to buy it, time passes, then you sell it. If you believe the stock will drop in price, you can reverse the order, selling shares, waiting for the price drop, then buying them back. During that time you own say, -100 shares, and are 'short' those shares.