The "Courbette" is one of the most impessive movements of the "airs above the ground". The horse rears up to its full height and performs several foward leaps on its hind legs, without its front feet touching the ground.
This movement is partically difficult for the rider to stay on the horse, but once it's mastered it was very useful in combat. Just imangine a foot soldier that is fighting against a soldier on horseback. The horse suddenly rears up, with the front hooves thrashing dangerously close to his head. Then the horse leaps into the air and the terrified soldier runs for his life in fear that he would be trampled to death.
It's easy to see why the courbette was so useful in battle and it's very entertaining and inspiring to watch.