Critical mach is a aeronautics term that refers to the speed at which some of the airflow on a wing becomes supersonic. When this occurs the distribution of forces on the wing changes suddenly and dramatically, typically leading to a strong nose-down force on the aircraft. This effect led to a number of accidents in the 1930s and 1940s, when aircraft in a dive would hit critical mach and continue to push over into a steeper and steeper dive. This problem is often lumped in with the catch-all phrase compressibility.
Wings generate much of their lift due to the Bernoulli effect; by speeding up the airflow over the top of the wing, the air has less density on top than on the bottom, leading to a net upward force. The relative difference in speed is due largely to the wing's shape, so the difference in speed remains a fairly constant ratio over a wide range of speeds.
But if the air speed on the top of the wing is faster than on the bottom, there will be some speed where the air on top reaches the speed of sound. This is the critical mach. When this happens shock waves form on the upper wing at the point where the flow becomes supersonic, typically behind the midline of the chord. Shock waves generate lift of their own, so the lift of the wing suddenly moves rearward, twisting it down. This effect is known as mach tuck.