What is the difference between reversible and irreversible controls?
Reversible is when there is a direct linkage from controls to control surfaces. For example the cable linkages in a light aircraft up to an MD-80.

Irreversible is when there is a hydraulic power control unit in the way, it can be mechanical or fly-by-wire. And such controls would sometimes need an artificial feel system to relay how much force is being applied.

It is found in airplanes that cannot be steered by just muscles.

A good way to picture it, is what happens if you move an aileron by hand, would the yoke turn as a result or no. Superman might be needed for a 747's rudder, but still, the rudder pedals won't budge.

More information here and here.



Source: airlinebuzz.com

Photo shows an unpowered rudder that was swung by the wind, in the cockpit the rudder pedals would show the neutral position, hence irreversible.