Plain English Meaning
The fastest speed at which you can make sudden, full control inputs or fly through rough air without risking damage to the airplane. Stay at or below this speed in turbulence, and the wings will stop flying before they can break anything.
Full Definition
The maximum speed at which the flight controls can be fully and abruptly deflected, or the airplane can encounter a sharp gust, without exceeding the airframe's structural load limits. Below VA, the wing will stall before it can generate enough lift to overstress the structure. VA varies with aircraft weight and is published in the Pilot's Operating Handbook.