Rich media ads contain images or video and involve some kind of user interaction. Where text ads sell with words, and display ads sell with pictures, rich media ads offer all kinds of ways to involve your audience with an ad--expand it, float it, peel it, you name it--and all kinds of aggregated metrics--number of expansions, multiple exits, video completions, the list is long.
While display ads may promote brand awareness, rich media ads drive and measure user engagement.