Power supplies are dull things. There's no denying it. No matter how many flashy lights or clever modular widgets you tack onto them, they won't make your PC faster, find the cure for cancer, or even make you more attractive to the opposite sex. However, don't think for one minute those unfortunate facts make the power supply less important than any other component in your computer.
Quite aside from the fact a very poor power supply can simply fail and destroy all the other components in your computer or potentially cause an electrical fire, even a decent but under-powered supply can cause a whole host of problems like random crashes and resets. So ensuring you choose the right power supply for your system is an important decision.
So, what should you look out for when choosing a decent power supply? Well, like many things in life, price is a good indicator - the more you pay, generally, the better you get. It's not always true but it's a good place to start. The weight of a power supply is also a good indicator. Power supplies are essentially built up from masses of big capacitors, magnets, and coils of wire. The more/bigger/thicker these components, the more power the supply can provide and the more efficient it is. Again, it's a rough rule of thumb but it's not often wrong.
Of course, these are only the basic indicators that should tell you it's probably best to avoid that lightweight bargain basement 400W model for your new gaming rig. When it comes to picking between which one of those expensive models to get, things get a little bit more complicated.
Most power supplies conform to an ATX specification of some sort, which is an open standard maintained by Intel. On www.formfactors.org you can read the full specifications should you have the time or inclination to do so. The specifications are guidelines as to what ratings each part of the power supply should be, their tolerances (the allowable level to which voltages can fluctuate) and other things such as over-voltage protection. Most modern day decent power supplies will conform to the latest ATX12V v2.2 standard (there's also another standard called EPS, if you fancy doing a bit of extra reading).