To clarify power phases, each 'phase' is just another link supplying power.
Think of it like a fire truck filling a swimming pool. If the truck uses all it's pumping pressure to power one hose, that hose will squirt water out at incredible pressure, and the hose will fly about all over the shop. If the truck were instead to run 8 hoses, pumping the same amount of water as before only evenly distributed among all 8 hoses, each hose would sit there nicely and fill the pool. Both methods fill the pool just as quick, but using the extra hoses makes the job smooth and controlled.
It's the same with power phases. The power phases supply power to the cpu. The more phases there are, the less power needs to be drawn from each one. The less power being drawn, the cleaner that power is.
There is of course a limit where adding extra phases just becomes a gimmick. A current 8 phase board with digital vrms can easily do the same job as a 24 phase board from a few years ago.
Not only that, but for it to really be relevant to you you'd need to be overclocking the crap out of your cpu anyway. If you only plan to run your system at stock then it all becomes irrelevant, and you may as well buy the cheapest board that has the functionality (read: the right slots, right features etc) you need.
