What type of training is insanity?

Maximum interval training. The classic interval training makes you go for high intensity for a shorter period of time than you go for light or medium intensity. Insanity makes you go the other way around: longer maximum effort (extremely intense) and then short breaks. It includes mainly cardio and plyometrics (jumping) + stretching. One might argue that there is a little bit of strength training (because of e.g. squats and push-ups). But, on the other hand, some people consider exercising a weight training only if you actually use heavy weights/dumbells. Depends on your definition of strength/weight training.