Plain English Meaning
The fastest you are allowed to fly with the flaps down. Go faster than this and you can damage the flaps or the wing.
Full Definition
VFE is the maximum airspeed at which the airplane may be flown with the wing flaps extended to a prescribed position. Exceeding VFE risks structural damage to the flaps, their attach points, or the surrounding wing structure. On the airspeed indicator, VFE is marked as the upper limit of the white arc.
Context Anchor
Seen in the aircraft flight manual or pilot’s operating handbook, on airspeed indicator markings, and during approach and landing when the pilot is deciding when to extend flaps.