How can I find out which ethernet cable goes where?

Finding out the "purpose" may be a bit of a stretch (other than the rather basic purpose of connecting network from point a to point b - how you use it may be different from the last occupant), but identifying the cables is a simple-if-tedious process of attaching something to one cable, and then plugging into all the other cables around the house until you find the end that connects, and repeating as needed. While you can buy special-purpose cable tracing tools, for doing one house it's generally going to make sense to just run around with a computer and find the cable that connects that way. Make life simpler in the future and label them as you identify them. It will be slightly faster if you connect something to each single cable, and then try each of the cables where they all come together until you find the one that connects, rather than plugging in one where they all connect and running all over the house to find the matching end. If any don't connect to the central point, find all the ones that do connect to the center and then try matching up any left-overs.

But, if you happen to have a multiport switch, you can plug that into all (or as many as fit) of the cables where they all come together, and then check which switch port becomes active as you plug a computer into each of the cables elsewhere in the house. This is the way they would normally be used, anyway. If they all work, you might not even care which one is which, so long as you have adequate switch ports to run them all (probably at least part of why they are not labelled now) since you can just plug into "the network" and not really care what port you are on, so long as it's just one network (common in most houses.)

I had a similar situation with a big bundle of plain CAT-5 cables in the basement. Each cable went to one random room in the house.

To determine which cable was associated with a room, I did the following simple experiment:

• In the room, twist together two of the conductors to each other. I connected orange to dotted orange, just because it was easy to remember. Doesn't matter which two you twist together.
• In the basement, for each CAT-5 cable, use an Ohmmeter to measure the resistance across orange and dotted orange. For every cable except the one where you connected the conductors, you'll see infinite resistance. For the one where you connected the conductors, you'll see no resistance.
• Don't forget to untwist the leads you connected.

An ohmmeter is built into any cheap multimeter like this $30 model from Radio Shack and since I had one around anyway for other electrical projects this was easier than buying specialized network testing equipment.