"Supercritical" is usually used with respect to wing design.
With almost any wing, the flow on top is accelerated to a speed faster than the free stream speed thanks to our friend Bernoulli. When you're flying near the speed of sound, the local flow on the wing can be be accelerated up to supersonic speeds. At that point drag really starts to increase. This is the "critical Mach number." If the local flow on the wing is accelerated 25%, then Mcrit will be 0.75.
A supercritical wing is able to delay an increase in the drag coefficient ("drag divergence") that accompanies transonic speeds when compared to a conventional wing shape. This is accomplished by reducing the local flow acceleration (smaller percentage) and forming weaker shocks (using a flatter shape).
A conventional wing and a supercritical wing may have the same critical Mach number, but the supercritical wing can tolerate a larger increase in the free stream Mach number before drag divergence is encountered.
(Edit: I forgot to mention that there is a tradeoff. Supercritical wings aren't great performers at slower speeds. I noticed on the F-8 page they mention that the 15,000 ft runway at Edwards wasn't long enough for the plane to land on.