The flight instructor of the helicopter reported that the student pilot was taking his second lesson, learning to hover over a grass area at the airport. The flight instructor was operating the collective and anti-torque pedals, while the student pilot was operating the cyclic. The student pilot made an abrupt rearward movement with the cyclic. The flight instructor increased throttle and raised the collected to gain height; however, the right rear skid contacted the ground, resulting in a dynamic rollover. The flight instructor added that there were no preimpact mechanical malfunctions with the helicopter and that in the future, he should initiate hover training at a higher height. Examination of the helicopter by a Federal Aviation Administration inspector revealed substantial damage to the main rotor blades, fuselage, and tailboom.