At the WWDC keynote, Apple went into discussion about the new features that will be coming to OS X Mountain Lion. One of these new features is the arrival of Game Center on to Mac computers from iOS.
Game Center for OS X will use the same account that users have created on their iOS devices, meaning no need to deal with separate accounts on various devices. It will also support play between Macs and will allow for crossplay between Mac and iOS devices. There will be support for turn based and head to head gaming.
For iOS device owners and Mac owners this greatly increases the potential of Game Center to be your central gaming hub. It will be interesting to see if they plan on incorporating their achievements system into games and apps created exclusively for Mac and distributed through services like Steam.