Tribros believe in Team Free Will. As opposed to fans who are particularly attached to one brother or the other, or to only Sam and Dean, or just Castiel, etc. Some fans identify as "tribro," indicating that they are devoted to the relationship between all three. It arose after the eleventh season finale of Supernatural when Dean clearly stated that Castiel is a brother, by fans who wanted to be clear they had affection for all three brothers.
Some Bronlies resent the term and mock it.