The explanations above are essentially the same thing, but with slightly different emphasis.
Mcrit is the lowest mach number at which the airflow at any point on an aircraft becomes sonic (mach1). The speed of airflow at any point on an aircraft is the freestream speed plus whatever acceleration the aircraft has given to it. So Mcrit is mach 1 minus the greatest acceleration found at any point on the aircraft. If for example the greatest acceleration is mach 0.2 then Mcrit is 1 - 0.2 = 0.8. So if we can reduce this acceleration we will increase Mcrit.
If we restrict our discussions to only the wings of the aircraft, we can examine the effects of increasing wing sweep. As air flows over the wings it must move apart, so that some passes over the wing and some passes under it. The acceleration given to the air depends upon the distance that the air must move apart (the thickness of the wing) and the time available for this movement to take place. The time available depends upon the freestream speed and the chord length.
If the wing is very thick with a short chord length, a large acceleration will be required. If however the wing is thin with a long chord length, the acceleration will be much less. So thin wings with large chord lengths will give high values of Mcrit.
Now if we consider a straight wing of moderate thickness and chord length, say 20% thickness to chord ratio. For any given angle of attack and freestream speed, this will give a certain acceleration of the aiflow passing over it. If we subtract this aceleration from 1 we will get its Mcrit.
If we now sweep this wing backwards, the aiflow will take a longer path over it. In effect we have increased the chord length without changing the thickness. This gives more time for the air to separate to allow the wing to pass through it. Subtracting this reduced acceleration from 1 will give an increased value of Mcrit.
A second way of looking at this situation is to consider the airflow over the wing as two components. One is at right angles to the wing leading edge, while the other is parallel to the leading edge. The flow at right angles to the leading edge experiences the same thickness to chord ratio as that produced when the wing was straight. But the flow parallel to the leading edge experiences no aerofoil section and hence no acceleration. So part of the velocity gets accelerated and the other part does not. Because only part of the flow is accelerated, the overall acceleration is less. Subtracting this reduced acceleration from 1 gives an increased Mcrit.
So whether we use the vector argument or the thickness to chord ratio argument, the effect is the same. Increasing sweep back angle decreases acceleration and so increases Mcrit. If we want to carry out accurate calulations we must use the mathematical method. But for most people the thickness to chord ratio argument is easier to understand.