I think it is a change in center of pressure, backwards, due to the shockwave when flying at high transonic speeds. This creates a pitch down moment which is unstable, since more pitch down, more speed, more mach, more shockwave, more pitch down moment... You could quickly go well into very dangerous airspeed leading to any number of undesirable compressibility effects, aileron reversal, fluttering, etc... and most likely structural failure.
Some airplanes are more prone to this effect, and have to augment their stability by means of a Mach trim compensator. I think the MD 80 family have them. I don't remember if that tendency has something to do with the tailplane, which is the cause of another unstable effect, the pitch up effect with can lead to the "superstall" and has a stability augmenting device of its own, the stick pusher.