Genesis was the son of the character associated with the X-Men called Cable, who came from the future. He had been abducted by the villain Apocalyse as a child and corrupted. Genesis was a time traveller who came from an alternate future of Earth, as did Cable.
Genesis sought to replace Apocoplypse and chose Wolverine to be a soldier in his army, the Dark Riders. He attempted to erase Wolverine's mind and re-bond adamantium to Wolverine's skeleton. On both accounts he failed. Wolverine's mutation was sent into overdrive and he reverted into a beast-like, almost simian form. Wolverine killed Genesis.