Plain English Meaning
Starting the engine by pulling the propeller through by hand instead of using the electric starter button. It's done when the starter doesn't work or the airplane was never built with one, and it must be done carefully because a spinning propeller can seriously injure or kill someone.
Full Definition
Hand propping is the procedure of starting an aircraft engine by manually rotating the propeller by hand to turn the engine over and initiate combustion, used when the aircraft has no electric starter or when the starter or battery is inoperative. The procedure requires a qualified person at the controls, proper chocking or restraint of the aircraft, correct throttle and mixture settings, and a trained person at the propeller using approved .