At least in modern pueblos, kivas are ceremonial rooms (always entered from the roof, and always round) used for religious rituals — generally associated with the kachina belief system. The kachina system seems to have emerged in the region around 1250 AD, but kivas themselves go back long before that — so apparently they’ve been “repurposed” from their original use.
Pueblo Bonito has no less than 32 kivas, and what you see here is a small slice of the largest one. It’s also located at the focal point of the pueblo.
By the way, did I mention that SOS will be playing host to the Four Stone Hearth blog carnival this week? It’ll be here on Wednesday the 20th, so if you run across any interesting anthropology blog posts today or tomorrow, please send them in!