Phase change is basically what your fridge is doing: you extract heat from the system (ie: the CPU, video card, etc) by evaporating a fluid. The fluid is then ran through a radiator (the get rid of the heat absorbed) a condenser (to make it liquid again) and a compressor (to increase its pressure). The fluid then gets heated again, evaporates, and the cycle goes on. It's called phase change because the working fluid changes phase (from liquid to gaseous and back).
If you remember Thermodynamics 101, you'll see that it takes a lot of heat to evaporate a fluid (much more than it takes to just increase its temperature when it's liquid), so phase change cooling is much more powerful than water- or air-cooling
As for liquid N2 cooling (I think that's what you meant), it's just cooling using a very cold fluid, such as liquid nitrogen (-330°F / -200°C). Not only is N2 very cold, but it will evaporate easily when heated, so LN2 cooling has a massive capacity. Of course, it's very expensive and unpractical for a desktop PC.
There's also Peltier cooling. This uses as peltier element, also called a thermo electric cooler. Essentially, it's two small blocks of semiconductor stuck together (also called a thermocouple). When you pass current through them, they develop a temperature difference, so you can use the cooler one to extract heat from another system. This is based on a quantum mechanical effect. Peltier cooling is not very efficient but it allows to cool a system below room temperature.
