The way I think of it is Mach No is the speed of sound,. In simple terms, below Mach 1, the air molecules can start to get out of the way before the ac arrives, above it they can't.
The speed of sound is a function of air density, the greater the density, the faster the speed of sound and vice versa, As you go up, the density decreases to the speed of sound decreases to so Mach 1 occurs at a lower airspeed so the Mach effects occur at a lower airspeed. Do I have it aright?