Overman was an alternate version of Superman from the parallel universe of Earth-17. Overman was created by the military as part of a corps of goverment superheroes. However, he contracted a virus that affected his mind, driving him psychotically insane. Overman proceeded to lay waste to his world and slaughter all its inhabitants. He ceased to exist during the Crisis on Infinite Earths.
During the "Second Crisis," Overman was accidentally re-created by the Psycho-Pirate, along with his favorite weapon, the Doomsday Bomb, which could obliterate planets. Animal Man, though extremely outmatched, was forced to take Overman on, eventually managing to trap him outside of normal reality.
Overman was a post-Crisis addition to the pre-Crisis universe, and was based on a character from a grim independent comic.