For most users, Game Center is all about matching up with friends and competing for rankings and checking out leaderboards. It's not much fun though if you don't have anyone to play against. If you've found a particularly cool multiplayer game in the App Store that you think a friend would like, Game Center makes it easy to tell friends about it complete with an App Store link for them to check it out.
That's all there is to it. Your friend will receive the email and be able to directly view the game on the App Store and choose to download or buy it.