term used by pilots. when accelerating quickly, the throttle is pushed all the way to the panel and the throttle lever (ball) actually touches the panel (wall). Hence, balls to the wall.

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.

Originally a military term for pushing maximum G-Forces in a jetfighter aircraft, as in pushing the ball of a throttle as high up as it will go (virtually touching the wall of the dashboard).

Fast; hectic; pushed to the limits

To go at full (unregulated) power

Steam engines had mechanical regulators that consisted of a pair of hinged lever arms with a ball on the end of each arm, as the engine sped up the centrifugal force caused the arms to raise up closing a valve. If you adjust the regulator so that the arms go to horizontal (with the balls pointing to the wall) without closing the valve you are not limiting the speed of the engine.

givin it all you got

Intense, extreme, to the max. The phrase comes from olde-fashioned steam engines; basically, they had two weighted balls attached to a vertical shaft which was connected to the engine. As the engine speed increased, these two balls would be raised higher because of centrifugal force! At top speed, they would be parallel to the ground, nearly touching the "walls" of the shaft! Hence, "balls to the wall."

Radical male homosexual underground nightclubs are rumored to have holes in the bathroom stall walls, through which a horny man would shove his erect penis, in hopes that a stranger in the next stall would give him fellatio. The hole was nicknamed the "glory hole". The horny man literally goes "balls to the wall" and hopes for glory. Participating so carelessly in a sexual act with a stranger who also participates carelessly in sexual acts with complete strangers is an profoundly extreme act in an age so rampant with venereal disease. The term is now used colloquially to refer to taking ANY action to its most extreme limit. The phrase is now synonymous with "taking it to the extreme limit" or "going as far as you can go" or... "going balls to the wall".