While engaged in an arguement with someone, and the arguement becomes public ( ie in an elevator and the doors open in the lobby) one person asks "Wanna hug it out?" and you stop the arguement and continue it at a later time, when it is out of the public eye.
Derived from Ari, on HBO's Series "Entourage"
Person A " I don't care what you think you're doing, I don't give a fuck anymore!"
Person B "Well it's none of your business anyway, Asshole"
(Elevator Doors open, and crowd boards)
Person A "Wanna hug it out? C'mon bitch, let's hug it out."
Person A and B mutually stop conversation until later time/date at which carrying on is appropriate.