Back in University, I always thought this meant agressively pushing someone against a surface. Later, with the adage of the internet and google (and yes university was a long time ago), I eventually learned this simply meant giving it your all. Ball wise.
The phrase “balls to the wall” actually refers to the centrifugal governor of a steam engine. This used used spinning balls to adjust a valve limiting the amount of steam entering the engine. As the engine sped up, pressure and centrifugal force of the spinning balls pulled them outward toward the wall of their housing. This activated a lever to limit the amount of steam.
So, if your balls were against the wall, that meant your engine was spinning as fast as it possibly could.
Even if the saying is actually benign, it attacts so much attention I haven’t had the nerve to try that phrase during some business meeting.