It's kinda of like the iTunes store, but for games. You make an account and when you buy games they get added to your account. By installing steam on a computer you are able to play all the games you own on that computer. There is no limit to how many computers you can access steam from.

I suggest you do what kindaallovertheplace suggested, make an account on steam and try Team Fortress 2. It's free to play so do don't actually have to spend any money to try Steam out.

My favourite parts about steam is that it's owned by Valve. Valve has a great reputation as a company and have continually shown that they value their customers. They are always trying to improve steam. It's also great because all my friends use steam as well. I nearly always use steam's voice chat over any system when I want to talk to my friends while playing.

My least favourite part is that you don't get a physical copy of the game. I like showing off all the games I own on my shelf but I can't really do that with steam. Depending on your internet you might find this to be a problem when downloading large games.