Can someone give a brief explanation of how the DC output rails work?

It is important to know that today's power supplies also work much different than older ones.

Older ones worked more like multiple power supplies inside of a power supply.

So you had 3.3 5 and 12 volt power supplies as well as the negative and standby power.

We are just going to look at the 3.3 , 5 and 12 today.

Old hardware before used to run on higher voltage and not take as much power so the lower rails had been used to provide these voltage. As power consumption started to rise it quickly became apparent we would have to move to a high rail to get the power we needed.

The reason for this is simple. Higher voltages require less current(amps) for the same wattage.

Quick math

voltage x current = wattage

and

wattage / voltage = current

So if you want to run a 125 watt cpu on 3.3 volts(you will quickly see why you do not do this).

125 / 3.3 = 37.878787.....amps

Well 33.9 amps, my old power supply can run that right? Sure it can, but the size of the wires would need to be increased or the number of them would need to be increased. An average house in US/Canada has 15 amps per circuit. and you already see the size of that wiring(14 gauge). Now think more about car wiring. It is bigger because it operates at lower voltage(12).

Speaking of 12, lets do the math for 12 volts.

125 / 12 = 10.41 amps. You no longer need larger wires.

Now your cpu runs on much less than 12 volts. The board has a high efficiency switching regulation system that will drop this 12 volts down to a nice 1-1.4 volts that most cpus need(and it can even be adjusted for different cpus and users).

So that is the basic reason for the move from heavy 3.3/5 to heavy 12 volt usage. Switching regulators negate most of the negatives of having to start at such a high voltage as well(linear regulators would have needed heatsinks the size of your case to do this job.).

In order to make new power supplies more efficient, they employ dc-dc(dc to dc) converters. So when the power supply runs it makes almost all of its power into a LARGE 12 volt rail. These lower rails are actually made off the 12 volts rail with dc-dc converters(these are another high speed switching regulator with very low losses). This allows better efficiency while still allowing older hardware that wants more 3.3 or 5 to run. If you load up the 3.3 and 5 volt rails, it will take some power from the large 12 volt rail, this is why they list a combined wattage for all the rails together.

These lower rails are still used, just not for power demanding devices. For example USB(and any hub powered devices) and SSD's all use 5 volts.

It is also the reason that a modern 350-400 watt power supply will run a system as good as the on in your image. This is why you have to ALWAYS check the 12 volt wattage or amperage(easy to convert to one another with math). Your power supply has a label for 750 watts, but will fail in places a good 400 will do the job.