The certificated flight instructor (CFI) was providing primary flight instruction to a student pilot in a tail wheel-equipped airplane. The CFI reported that he demonstrated the first landing, and the following landings were conducted by the student pilot. On the third landing, the airplane touched down on the main tires "straight, with no bounce." During the landing roll, while the tail wheel was still off the ground, the airplane veered slightly to the left and the student pilot applied left rudder. Subsequently, the airplane veered sharply to the left and the student pilot applied full brakes. The airplane exited the runway and nosed over. The airplane's wings and rudder sustained substantial damage. The pilots reported no mechanical failures or malfunctions prior to the accident.