With Game Center, you can play your favorite games with friends who have an iPhone, iPod touch, iPad or Mac. Game Center is also where your global leaderboards, achievements, challenges, high scores and other data are stored for each Game Center-compatible game you play.
Some people also find this particular feature a major nuisance over being bugged with notifications and invites for the games they no longer have installed on their device.
Thankfully, you can easily remove any game that you no longer play from Game Center with a quick swipe.