The power supply is the piece of hardware that converts the electricity coming from the wall socket into usable power for the many components inside the computer case.
Power supplies explained
It converts the alternating current from your wall socket into a continuous form of current, called direct current, which is needed by the computer components. It also regulates overheating by regulating the voltage, which can change automatically or manually, depending on the power supply.
The power supply is a crucial component, because without it, the rest of the internal hardware cannot function. Motherboards, cases, and power supplies all come in different sizes, called form factors. All three must be compatible to work well together.
CoolMax, CORSAIR, and Ultra are the most popular manufacturers of power supplies, but most of them are included with the purchase of a computer, so you only have to deal with the manufacturer when you replace the power supply.