Plain English Meaning
The fastest speed at which you can yank a control fully in one direction without risking structural damage to the airplane. Slower than this, the wing will stall before anything breaks; faster than this, you could bend or break the airframe.
Full Definition
The maximum speed, established by the aircraft designer, at which a full and abrupt deflection of any single primary flight control may be made without exceeding the airframe's structural load limits. Above this speed, abrupt control inputs or strong gust loads can overstress the aircraft; below it, the wing will stall before structural damage occurs. Design maneuvering speed is symbolised Vₐ and typically decreases as aircraft weight decreases.