“Balls to the wall” supposedly refers to pushing the throttle levers of an airplane (which are topped by ball-shaped handles)fully forwards (against the wall of instruments and controls), which is the max power position.

Actually, much older than that, I've heard - ever look at an old steam engine? That bell shaped thing on the top? Inside of that are two balls that spin out to the wall of the bell, which pushes a lever to reduce the steam pressure, topping off the speed of the train - thus balls to the wall means all out, top speed for the train.