A stargazer is a horse that carries its head excessively high when being ridden. The head is often close to horizontal and the horse is looking up at the sky.
Stargazing is often associated with the horse hollowing his back away from the rider - uncomfortable for both individuals. It can be caused by a bit that is too harsh, a poorly fitting saddle or a rider with heavy hands. It's also often seen in unfit animals that are struggling to carry the rider's weight.