With maximum effort, energy, or speed, and without caution or restraint. The phrase most likely originated as an aviation term, referring to the throttle levers of military aircraft (which have a rounded ball on top) being pushed to their maximum limit (i.e., to the bulkhead, or "wall"). While it does not in fact refer to testicles, it should be used with caution because of this popular association. Look boys, this air raid needs to be done fast and efficiently; fly in balls to the wall, hit the targets, and get the heck out of there.