Plain English Meaning
VFE is the fastest you are allowed to fly with the flaps down. Go any faster with the flaps out and you risk damaging them or the parts of the wing that hold them on.
Full Definition
VFE is the highest airspeed at which the airplane may be flown with the wing flaps extended to any approved setting. Exceeding VFE while the flaps are deployed can overstress the flap structure, the flap tracks, or the attaching hardware, and may cause structural failure or asymmetric flap problems.
Context Anchor
You will see VFE in the airplane’s operating information, on airspeed markings, and during procedures such as approaches, landings, and where flap use may be considered.