A three-way couple in a long term relationship
Mike, Rick and Steve have been together for six years. They're a trouple.
A couple who has a friend that is always with them becomes a trouple. The third person has to be friends enough or have been hanging out with the couple long enough to not feel like a third wheel, thus becoming a trouple.
It was decided that Gary was part of a trouple when he went with Frank and Tracy to Las Vegas.
It is a combination of "couple" and "triple" where the three individuals are in an equally inclusive relationship.
Tim, Pat and Lawrence all live together and share a california king while they enjoy being a "trouple."