Lots of detailed answers but the main gist is that the amount of energy that goes into changing 1g of a liquid to a gas (when it's already at its boiling point) is orders of magnitude greater than the amount of energy it takes to heat 1g of that liquid to its boiling point. So making use of a phase change means you don't need to use as much refrigerant. Less space taken up, less cost of expensive refrigerant, etc.