Refer to figures.
LOW ALTITUDES

Indicated Airspeed (IAS) is not truly a measurement of the speed of air particles, it is instead a measurement of dynamic pressure, and this can perhaps be thought of as the amount of air particles flowing past the aircraft per second. It does, therefore simplify the lift equation quite significantly, and this is why we use it for our primary speed reference during low speed flight. It is a direct indication of how much lift/drag our aircraft can produce.

• lift = (½ x rho x V²) x S x C_L 

But as the indicated airspeed is an equivalent measurement to ½ x rho x V² (which is the dynamic pressure), this means the lift equation is instead:

• Lift = IAS x S x C_L

Where S is the wing area and C_L is the coefficient of lift, a dimensionless measurement that allows us to work out how much of the dynamic pressure the wing is transferring into lift force.

Knowing that, at the stall in straight and level flight, Lift = Weight and the C_L is at its maximum (C_LMAX) the stalling IAS is calculated as follows:

• Stalling IAS = Weight / (S x C_LMAX)

Notice that nowhere in this equation is altitude mentioned. This is because altitude difference is already accounted for in IAS, so stalling IAS does not change with altitude, when at low altitudes.

HIGH ALTITUDES

For a constant IAS, as altitude increases, the true airspeed (TAS) increases.

This means that, at high altitudes, even a low IAS is equivalent to a much higher TAS, and above around 300 kt TAS, the effects of compressibility begin to change the fundamental airflow characteristics. 

In essence, compressibility is where the air doesn't have enough time to notice the wing approaching and get out of the way, so it gets squashed and has to act more quickly, taking more energy out of the air, and this reduces the critical angle of attack, thereby decreasing C_LMAX and meaning that stalling IAS increases.

You can see this effect on the graph above.