One of the best parts of the iPhone, along with the whole phone thing, is the fact that it's got a vast App Store with plenty of games out there. In fact, they've got a monstrous list, at 50,700 total games, and it rakes in somewhere in the ballpark of $500 million in revenue for the company. So, obviously mobile gaming is something that Apple wants to capitalize on, and sure enough, they've introduced Game Center for iPhone OS 4.0.
The entire idea is social gaming. While many might consider this similar to the PlayStation Network, it's more akin to Microsoft's Xbox LIVE Arcade, in which you get to play a lot more "casual" games. Even if there are leaderboards, and we know there's competitive people out there, the main focus is to be social with the people you know playing inside the same gaming network, along with meeting new friends.
Additionally, with multiplayer games being the focal point here, your'e going to be able to meet up with people of your own "skill," as you move from one title to another. This is a lot like the TrueSkill meter that (almost) every multiplayer game known to man uses, at least in the console gaming world. The whole system will track game-specific achievements as well. You can also add friends to a growing list, if you like meeting strangers.