Plain English Meaning
It's the fastest speed at which you can yank the controls hard without breaking the airplane. Above this speed, an abrupt control input could bend or damage the structure. Below it, the wing will stall first and protect the airframe.
Full Definition
The maximum speed at which the airplane will stall before exceeding its design load limits when full or abrupt control inputs are applied. Below VA, a sudden full deflection of the flight controls or a strong gust will cause the wings to stall before the airframe can be overstressed. Above VA, the same input can produce structural damage. VA changes with weight: it is published for maximum gross weight and is lower at lighter weights.