OMG is a centralized trophy awarding system for your computer. Take an example of games. Many games have a concept of badges, trophies, medals etc. All these are managed by the game themselves and are locked into the games itself. OMG is made to have a central area where all the medals, trophies, badges etc are managed. The game is freed from managing it and the game developers can spend more time on making the game even more awesome.
OMG is not limited only for games. Even application can register their trophies. In OMG trophy is a generic term which encompasses badges, trophy, medals etc. For example Tomboy can award the user a Trophy of "Tomboy beginner" when the user creates the first note. "Tomboy Addict" can be used for person who has more than x notes. Your web browser can award you a trophy of "Ars fanboy" if you visit "Ars Technica" too often.