The maneuvering speed is the maximum calibrated airspeed at which - starting from straight and level flight - you can safely move any single flight control from the neutral position to the maximum deflection possible at that airspeed.
What constitutes full deflection varies from aircraft to aircraft, and also - frequently - with airspeed. At low speeds, it is generally limited by the control surface's mechanical stops (those thingies which physically block the control surface in question from moving to a greater deflection); at higher airspeeds, depending on the aircraft, it can be limited by an additional, moveable mechanical stop (which limits the control surface to a smaller and smaller range of deflection as airspeed increases), by the amount of force available with which to move the control surface (in which case, at high speed, the control surface's actuators are physically incapable of deflecting the surface past a certain amount, and the possible range of motion decreases as airspeed increases), or, in some cases, by the mechanical stops for the yoke, joystick, or rudder pedal (for aircraft in which control-surface deflection at high airspeeds is limited by a mechanical ratio adjuster, such that, say, turning the yoke all the way to its stops commands less and less aileron travel as you go faster and faster).
The maximum speed at which a full-scale deflection in the pitch axis is safe is frequently different from the maximum speed at which a full-scale deflection in the roll axis is safe, which is, in turn, usually different from the maximum safe speed for a full-scale yaw input. The maneuvering speed of the aircraft as a whole is the lowest of these speeds (which is generally the limiting speed for the pitch axis).
Note that being at or below maneuvering speed only guarantees that a structural failure will not occur if, starting from straight and level flight in an undamaged aircraft with all control surfaces originally in their neutral positions, one single control surface is deflected to its limit. If you start out in an aircraft weakened by undetected fatigue damage, or if you push two or more control surfaces in different axes to full deflection simultaneously, or if you take a control surface from full deflection in one direction to full deflection in the other (especially if done multiple times in a row) rather than merely from the neutral position to full deflection in one direction, continued airframe structural integrity is not guaranteed. To quote Wikipedia:
It has been widely misunderstood that flight below maneuvering speed will provide total protection from structural failure. In response to the destruction of American Airlines Flight 587, a CFR Final Rule was issued clarifying that "flying at or below the design maneuvering speed does not allow a pilot to make multiple large control inputs in one airplane axis or single full control inputs in more than one airplane axis at a time". Such actions "may result in structural failures at any speed, including below the maneuvering speed."