To push to the limit, go all out, full speed.
A very colorful phrase, one needs to be careful when using "balls to the
wall". Although its real origin is very benign, mos people assume it is a reference to testicles.
In fact it is from fighter planes. The "balls" are knobs atop the plane's throttle control.
Pushing the throttle all the way forward, to the
wall of the cockpit, is to apply full throttle.