What is tribal style belly dance?

Tribal belly dance has its roots in folkloric and traditional belly dance, and is a recent innovation in the dance. It's really taken off within the last ten to twenty years. It has spread from the West to the East coast and evolved as it went. There are many flavors of tribal, from fusion (although almost all tribal is technically fusion) to ATS to what I like to call "SCA folkloric." An excellent and extensive overview of tribal and its history is available here.

American Tribal Style belly dance uses "structured improvisation" - the dancers use small nonverbal cues to tell each other what they're going to do next. It does not use choreography (except on rare and specific occasions). The beauty of ATS is in the synchronization of the dancers and the elegant and powerful movement vocabulary.