The large increase in drag is caused by the formation of a shock wave on the upper surface of the airfoil, which can induce flow separation and adverse pressure gradients on the aft portion of the wing.
In early development of transonic and supersonic aircraft, a steep dive was often used to provide extra acceleration through the high-drag region around Mach 1.0.
This steep increase in drag gave rise to the popular false notion of an unbreakable sound barrier, because it seemed that no aircraft technology in the foreseeable future would have enough propulsive force or control authority to overcome it.
Two of the important technological advancements that arose out of attempts to conquer the sound barrier were the Whitcomb area rule and the supercritical airfoil.
These, along with other advancements including computational fluid dynamics, have been able to reduce the factor of increase in drag to two or three for modern aircraft designs.