Phase cooling is short for Phase Change... it means that the cooling apparatus takes a liquid with a very low vaporization temperature and applies it directly to a specialized CPU heatsink. The liquid then evaporates, and the LHV (Latent Heat of Vaporization) absorbs a lot of the heat energy from the CPU during the phase change. The gas is then recycled back into the cooling apparatus and condensed using extreme refrigeration methods to a liquid form, and the leftover heat is expelled out the back of the unit.
The layman's version is that vaporization of a liquid to a gas carries away more heat than simply heating the liquid/gas does alone (the same way sweating is used to cool the human body), and so this is adapted to processor cooling.
I'm not sure what substances they use for it, so I can't tell you the exact operating temperatures... but they could potentially range from room temperature to far into the negatives depending on what they use. Liquid Nitrogen wouldn't appear in a phase cooling system, since it's too cold to produce in a compact unit.
It should be noted, that while colder temperatures make your processors happy, they can also decrease its life span. If the temperature gets too low, it induces stress in the processor and other components which could cause it to die early or even crack.