This term was NOT defined by Ari from HBO's Entourage nor does it mean to end a conversation/fight, temporarily, with a hug. It simply means do you want a hug? Also, it was used in a Thanksgiving holiday episode ("The One Where Chandeler Doesn't Like Dogs), in 2000, my Jennifer Aniston's character, Rachel.
While talking about a break-up her subordinate is going through:
Subordinate: Hey. Thanks for talking with me
Rachel: C'mon. What are bosses for? Hug it out!