As symsus said. A PSU is a power supply, and PSU stands for power supply unit. It takes voltage from your wall sockets, and converts it to voltages which your computer system can use, mainly 3.3V, 5V and 12V.
There are three types of PSUs when it comes to cabling - a fully modular PSU allows you to attach the cables necessary, and reduces clutter. A semi-modular PSU essentially a fully modular PSU except it has a couple of attached to the unit, normally important ones such as the motherboard 24-pin and CPU 4/8-pin cables, as opposed to being able to be attached. Non-modular PSUs have cables attached to the unit, and can get quite messy, and result in difficult, and possibly messy cable management as well. Good cable management is...