A PSU supplies several different voltages. in general all you need to worry about is the 12 volt supply, the others are rarely used and if your 12 volt supply is fine they will be too.
When someone says a 750 Watt supply only outputs 650 Watts at 12 volts that's exactly what they mean. Basically some lower quality manufacturers will add the other voltages in. So it may. be labeled 650 Watts on the 12 volt supply and 100 Watts on 5 volt. A good manufacturer will generally have the 12 volt supply able to deliver all 750 Watts at 12 volts. In addition some will make a supply, label it as 550 watts and it will burn out at 400 Watts. so badically they lie. they may also have issues with power quality, efficiency, and voltage regulation which can cause system problems. the protection circuits can also be low quality which means if it Burns out it can take other components with it. So it is very important to go with a quality manufacturer. OCZ, seasonic, corsair etc. there are also professional reviewers who fully test them till burnout and take them apart. jonnyguru and hardwaresecrets are two.
As for "rails" these came out of an outdated safety standard, bad marketing departments, and crossfire/sli. a PSU only has ONE 12 volt supply. What they do is they put a several current limiters in between the groups of wires and the supply to break them into groups. Current is your amps. so the 12 volt supply may be 600 Watts. volts x amps = Watts. so the total 12 volt supply can handle 50 amps. to get the "rails" they might create 3 groups of connectors limited to 20 amps each. Usually this would be the motherboard supply, and two connections for graphics cards.
Now, they do this so they can one up eachother in the number of rails or say "3 20 amp rails" etc in marketing. This is dishonest because if you add up the rails its far more than what the supply can deliver. Its also a pain to use because you have to keep track of what is in what rail, and you can run into situations where you have to split a GPU across rails, or you have enough power, but the rails artificial limits prevent you from using a GPU.
There's also 80 plus ratings. the higher the rating the less power is wasted and turned into heat in the PSU, and the lower the electric bill. in general 80 plus bronze is good enough for most people unless its going to be on and under load 24/7.
So in short, you want a good highquality brand, you want to check reviews, you want a supply that has a SINGLE high current 12v rail that ideally is rated at the same or close to the same as the actual PSU rating, and want it to be 80plus rated. And of course want enough wattage for your system. That can vary a lot depending on other components and future proofing, and is a common question which people will be happy to help you with in the forum.