'Local supersonic flow' says it all really.
Because air is accelerated over the upper surface of the wing, there are regions where the flow becomes supersonic over a conventional aerofoil even at Mach numbers as low as about 0.4.
Transonic (or 'compressible' flow) flow is generally bad, because energy has to be put in to compress the air, and this wastes a lot of energy. (The air is heated as it is compressed, then some of the heat is dissipated, so that energy used to compress it is 'lost'.
Local supersonic flow is more serious, because shockwaves develop, and this produces 'wave drag', which is very significant, so most civil aircraft are designed to minimise these effects.
The two traditional approaches to this are:
Sweeping the wings - This effectively makes the air move diagonally over the wing, so that the component normal to the wing is slower than the free stream velocity. The component parallel to the wing essentially has no effect. This clearly incurs a penalty in that a swept wing is not as effective per unit wing area as an unswept wing.
Supercritical wing sections - More recently, wing sections have been developed which reduce the 'peak' velocity over the wing and distribute it more evenly, thus delaying the transonic drag rise. These sections are less efficient than conventional sections, but sweep angle can be reduced, yielding both structural and aerodynamic benefits. (Compare the sweep on a 747 with that of a more modern aircraft!)
As for the sonic cruiser, I can't believe that there will be no local supersonic flow, so I am keen to find out what Boeing's solution will be. It all sounds like pie in the sky at the moment though. (Mmm.... Pie!)
Pie