Acronym for Power Supply Unit.
Generally, the bit that takes 240v AC and turns it into the various levels required inside the computer.
PSUs can range from 1.5 volt wall-warts (those little black boxes intended to hang out of a wall power supply) right up. The biggest power supply I have is a two part unit, with a single phase rectifier and then a 440 volt PSU for an ancient photograph enlarger, which was used in printing photographs to paper.
PC power supplies range in quality from a $50 taiwanese crapper to a $500 Lian-li or seventeam or antar item.
The differences come from:
PSUs for computers these days are ATX which means they have a unique 20 pin motherboard connector. ATX PSUs for Pentium 4 and other recent motherboards have two more connectors to provide 12V and ground to the CPU. The cool thing about ATX is that the power switch is only 12V and is connected to the mainboard, not the CPU. Because ATX power supplies are always on, they always supplies a low current to the mainboard in ATX, so don't change ram or IO cards or CPUs without unplugging the mains first. This latter is also a disadvantage as the case and system are no longer grounded to earth through your power cord, so you have to be very carefull with statically sensitive equipment (in case of a computer, everything but the physical chassis/case is a good guideline).
Older PSUs are often AT, in which there are a pair of motherboard connectors, which are almost always labelled P8 and P9. Sometimes a third connector is present for multi-CPU machines. The biggest irritation for AT PSUs is that the power switch is a 240V switch, and is wired to the PSU. An advantage of this is if you turn the computer off, it is off. A disadvantage is that changing the PSU can get fiddly near the power switch, and if you have a dodgy switch may cause a bit of a shock.
Note - Compaq, Dell, and Gateway are renowned for using strange PSU standards.2?3? If you need to replace a PSU in one of those brands then check very carefully. The good news is that the stock PSU is very well engineered. In some cases with these types of machines, it may end up that replacing the case and PSU is a cheaper alternative (as in the case of most Gateway computers).
Some cards have power connectors on them too - I've seen an ancient MFM hard drive controller and a modern FireWire card and a modern SATA controller with Berg connectors for power. Presumably these cards would draw too much current from the ISA or PCI bus.
1? More commonly known as Molex connectors after their inventor/manufacturer
2? In the case of Dell PSU's it's possible that they've 'shifted' one (or more?) wires from the ATX connector to one of the other connectors. So in theory it should be possible to hack a 'normal' PSU and turn it into a 'Dell' PSU :) Probably not worth the bother though. According to other sites, models from the Dimension 8250 up use standard ATX PSUs, so replacement of these models is fairly straightforward.