Plain English Meaning
The speed range where some air flowing over the airplane is moving slower than the speed of sound and some is moving faster than the speed of sound at the same time. It is the messy zone between fully subsonic flight and fully supersonic flight.
Full Definition
The range of airspeeds, roughly Mach 0.75 to Mach 1.20, in which airflow over different parts of the aircraft is partly subsonic (below the speed of sound) and partly supersonic (above the speed of sound) at the same time. This mixed flow produces shock waves on the airframe and can cause buffeting, control difficulties, and changes in .