To put it easily, Steam is to PC games, what iTunes is to iPhone apps.
Like the iTunes store, you purchase your games through the Steam store (although, you can also purchase retail, than register on steam).
Like the iTunes store, multiple developers sell their games through Steam.
Like the iTunes store, Steam keeps all your games up to date for you.
Unlike the iTunes store, Steam must be running in order to play the game. However, there are built in community features like friends list and chat that allow people to sent you messages in any Steam game, great for scheduling a game in Left 4 Dead when your currently in Bad Company.
You can also download Steam on any computer anywhere and log in with your account to play your games. Your not limited to the amount of installs or forced to have a CD in the drive (this has been amazing for me when my hard drive crashed, didn't have to baby sit CD installs, just logged into steam and re downloaded all my games overnight).
You don't need to keep steam running ALL the time, just when you want to play games purchased through steam. Although, I've grown to love having steam running all the time simply so I can see if any my friends are currently in game so I can join them.