When talking about Mach, it is pretty common to relate it with supersonic aircraft, but not always. This number of airflow velocity helps to determine the limits of the aircraft performance in terms of maximum airspeed.
The critical Mach number (Mcr) is the lowest Mach number of the plane in which the speed of sound is reached (Mach=1) at some point in the aircraft (it could be anywhere on the aircraft surface).
The fact to know is that the aircraft when reaching a certain speed (overall speed of the aircraft motion), the aircraft over some points reaches speeds above the overall registered in cockpit airspeed indicator, this is due to the different shapes and curves or airfoils on the aircraft. Therefore, the airflow travels at different speeds in the aircraft body.
But why is this important? Well, if any airflow reaches the speed of sound, it produces shock waves, causing an increasing drag, lowering the aircraft speed and reducing the performance and control. Here is one why it was difficult to overcome the speed of sound at the early aircraft.
Explanation, the aircraft is designed considering all these facts, and ensuring the airflow over the surfaces not reaching the effects of the shock waves. The airplanes in regime supersonic (interceptors, fighters, etc.) are designed to take care of this number and to overcome the Mach 1 (overall airspeed), designed with thin surfaces, and these supersonic aircraft even have their Critical Mach is less than 1.
There is complex work in designing shapes for supersonic and transonic speeds reducing all the shock waves impacts on the aircraft surfaces. Therefore depending on the mission for the plane and the model.
About the cover photo, the plane of Nasa, it is a Vought F-8A, testbed aircraft (designated TF-8A) to install an experimental Supercritical Wing (SCW) in place of the conventional wing. The wing configuration reduces the effect of shock waves on the upper surface near Mach 1. Therefore, it reduces drag.