Yes, thats how power lines work, they transform a pretty high voltage, to a nuts voltage in the reigon of 16-17kV and send it over the cables, when it gets to your substation, if youve seen one, theres a big block looking thing, that transforms the 16-17kV down to a useable 230v (115v America). But it can also work in reverse, your comptuer PSU. Capacitors are basically like a storage of energy, a big one can be big enough to power things, alot of Car modifiers use Caps, an extreme form might I add, of around 1-2 Farads which stop the thudding bass dimming the headlamps! Capacitors are also used in computers which are very small around Nanofarads-MicroFarads. When charged, these can keep a steady power source, even if the input fluctuates, the capacitors keep it nice and stable. That PSU is basically using a transformer from 230v to 12v and then using charged capacitors to keep a steady power source, it also has advanced electonics using diodes to switch Alternating Current to a steady Direct Current. The reason it connects to your other PSU is for a control line to work off so it turns on with your primary PSU, and accepts AC voltage to transform, which in turn means your GPU is able to have a good power source apart from your main PSU and so there is no Power problems.
Sorry to bore you! If you are still reading here, my word you must have nothing better to do
Hope this clears things up
Edit
You guys don't get it...
You can take a very small amount of power, and make it into a very large amount of power. This can be done through large capacitors and transformers.
Depends on what you mean by large amounts of "power" yes, you can smack up 12v Volts to over 100kV quite easily, but that doesnt mean that has any more "power" it jsut means it has more volts compared to more amps! Our 12v rails usually run at 20amps@12volts, doesnt mean its more than the 13a@230v we have out of wall sockets, its all proportionate! As Voltage increases Amperage decreases proportionatly, and as Amperage Increases Voltage increases Proportionatly! (Probably a crap explanation)
Ruan