This word is now a noun as well as an adjective. It refers to a person whom you meet 'randomly', or whose identity or relation to anybody else is unknown. It is often used to refer to people you meet at parties or on nights out, whose names you don't know or forget, and whom you never see again.
You can also say 'random guy', 'random girl' etc.
"Who's that guy standing in the background of this photo with a mop on his head?"
-- "I dunno, just a random who followed us in off the street, I think. He slept in the shed."
"I didn't really know anybody there so I was just chatting to randoms all night."