Badges shows other Users how active you are at AMD Forums. Also, I believe, Badges is one of the reasons that determines your rating at AMD Forums.
You don't earn anything physical such as hardware or discounts etc. It simply a means to show you how you are doing at AMD Forums compared to other Users.
The old AMD Forums you were awarded points concerning which category you qualified. Thus you can tell where you stand in respect to other Users. For instance if you were very active at AMD Forums you might have found yourself in the Top Ten or twenty list of Users at AMD Forums.
Also in the old AMD Forum other Users can award you a Badge such as a "Thank You" Badge or "Well Done" Badge etc. and be able to transfer points to you from their own point amounts.
But since the new AMD Forum format came out, the Point system was eliminated replaced by different form of Badges and Kudos and other categories that determines your eventual rating at AMD Forum.