Game Network allows access to 3rd party libraries that enables social gaming features such as public leaderboards and achievements. Currently, the OpenFeint and Game Center (iOS only) libraries are supported.
If you want to use both OpenFeint and Game Center, iOS OpenFeint will post achievement updates and leaderboard updates to Game Center provided OFGameCenter.plist is present in the project folder. See http://support.openfeint.com/dev/game-center-compatibility/ for details.
Staring with build 2012.725, Game Center has been added as a standalone provider for iOS apps (without the need to use OpenFeint).
Note: Adding "require gameNetwork" to your code will enable Corona Launchpad regardless of the setting in config.lua.
For more information on OpenFeint, see the OpenFeint guide.
For more information on GameCenter integration, read the tutorial on the blog. Also note that the nomenclature used in the Corona APIs for Game Center attempt to match the official Game Center APIs as much as possible. This will allow you to cross-reference with official Game Center documentation.