Evaporation of a liquid takes away heat. As the rubbing alcohol evaporates it absorbs heat and creates the cool feeling.
Pressure is proportional to temperature.
The contents of the aerosol can are under pressure at room temperature. When you spray the contents out, the contents are able to expand and there is a decrease in pressure. Because there is a decrease in pressure, there is a corresponding decrease in temperature. The liquid refrigerant flows through an expansion valve. The decrease in pressure corresponds with a decrease in temperature.