Cletus Kasady, in prison for multiple murders, shared a cell with Eddie Brock a.k.a. Venom. When the symbiote broke Eddie out, it left behind its "son" which bonded to Kasady. And thus, Carnage was born. An interesting fact is that the bond between Kasady and Carnage is much more profound than that of Venom, as Carnage/Kasady refer to themselves as "I" rather than "we"; this may somehow be due to Carnage bonding to Kasady's bloodstream as opposed to his skin, though there's no direct evidence of this. Carnage is also more powerful, violent, deadly, and very likely more insane than its parent—this could also be due to its host, who was a psychopath even before the merging. Carnage also had its own offspring that became Toxin.
Carnage is red with yellow teeth and white eyes, and appears to have tentacles coming out of its back. He also has claws.
Carnage can generate tentacles, swing lines, and even bladed weapons. He also has superhuman strength, speed, and agility.