Anything that truly does not make any sense of any kind whatsoever or seems dreadfully out of place, usually in a comic light; as though it were literally placed at random.
Also pertains to entertainment in the sense of a random film or CD, for example, Johnny Cash does "Personal Jesus"! That's just, so random!
A large blue light hovering above the Marlboro man playing "Funkytown" on his CD player with gangsta rappers coming out of his ears and a monkey dancing on the end of his penis? That's so random!