Cryogenic Separation is a distillation process that occurs at temperatures close to -170 degrees celsius. At this temperature, air starts to liquify.
Before separation can occur, there are specific operation conditions that must be achieved. Distillation requires two phases, gas and liquid. Air must be very cold for this to happen. For this instance, at one atmosphere, nitrogen is a liquid at -196 degrees celsius. A pressure 8-10 times atmospheric pressure is required for this process. These conditions are achieved via compression and heat exchange; cold air exiting the column is used to cool air entering it. Nitrogen is more volatile than oxygen and comes off as the distillate product.
A cryogenic air separation plant is expensive and large; the distillation column is several stories high and must be well-insulated. Consequently, it only becomes economically feasible to separate air this way when a large amount is needed. Cryogenic separation is also capable of producing much purer nitrogen than either of the other two processes because the number of trays in the distillation column can be increased.