Game Center was first introduced at WWDC 2010, it was originally going to be included in the iOS 4.0 update but was not released, it was then released in iOS 4.1 for iPod Touch 2G or later (iPhone 3G was did not officially get Game Center) and iOS 4.2.1 for iPad.
Game Center lets friends, and soon-to-be-friends, in on all the action. Invite someone to join, then get a game going. Or choose to go up against people you don’t know from anywhere around the world in a multiplayer game. It’s your world. Everyone else is just playing in it.