I've just re-read the post title (a classic case of RTFQ) and realised you were asking about "supercritical" aerofoil designs, not wing sweep.
The supercritical wing uses a larger nose radius and flatter top surface than conventional designs. This provides a lower air velocity over the top of the wing and so delays the onset of shock waves on the top edge of the wing.
This means a far lower wave drag at transonic/supersonic speeds, much weaker normal shockwaves and less tendency to experience mach tuck.
The surprising thing, for anyone who knows anything about aerodynamics, is that there is very little trade off against low speed performance. The supercritical wing actually performs extremely well at low airspeeds, due to the large leading edge radius and relatively high thickness to chord ratio.