PSU is short hand for "Power Supply Unit" aka power supply.  The power supply is usually located on the top of the computer case (unless it is a laptop) and is where the big power cord plugs in to the case (the one with three prongs).

The power supply turns the AC power from your house / office into DC current for the various bits inside your computer.

The power supply is one of the most likely parts to go bad and die on a consumer level computer.  Computer manufacturers take short cuts to save money and a cheap power supply is usually thefirst places they cut corners and hope thePC lasts until the warranty expires.

A good power supply can significantly increase the lifetime of your computer, but they come at a cost.