How would one define or explain the term "unloading the controls?"
When maneuvering the aircraft by deflecting the control surfaces with the stick, the wing with the downward aileron and the tail will generate additional lift, which increases the load on that wing (using the ailerons) and on the tailplane (using the elevator).

Unload the controls is a request to neutralize the pressure on the controls. Usually this means bringing the stick back to the center position, reducing the controls surface deflection, the amount of lift generated, and therefore reducing the aerodynamic load on the wings and tailplane.