Mach number = Airspeed / Local Speed of Sound
Speed of sound = K * SqRt (Absolute Temperature)
Therefore, as you go up, the ambient temperature drops.
As the temperature drops, the local speed of sound drops. Your airspeed, remaining constant as measured in knots, becomes closer and closer to Mach 1.
So, on the first equation above, "Airspeed" starts off small relative to "Local Speed of Sound", so "Mach number" is small. The top of the fraction remains constant, but the divisor gets smaller and smaller as you climb. Hence the overall value of the equation increases.
Does that explain it?