The story starts with a guy named Tim Langdell, who started a company a while back named Edge Games. Since he founded that company, he has mercilessly gone after any other game company who dares to use the word "edge" in their title, claiming that he has the trademark to any and all "edge"-related gaming. He's gone after EA's Mirror's Edge and a few other titles, but the App Store has been a prime target, where he simply contacts Apple, claims the app is in violation of his trademarks, and gets apps pulled without a problem. The latest target is a title called Killer Edge Racing by a company named PuzzleKings, and reportedly Langdell has gone so far as to trademark that name, despite the fact that the game using it has been around for years.
Hence the indie game developers' "edge-volution." They aren't actually renaming their games in the store, just showing off solidarity with other developers against what they see as Langdell's wrongdoing, and getting the word out about his actions against "edge" on the App Store.