Acronym for Uninterruptable Power Supply.
Roughly speaking, this is a big battery that will run your computer for a short time when the power goes out. It isn’t usually large enough to maintain power to the computer for an extended length of time (hours) (unless your money:IQ ratio is too high, or, like zcat, you've been given four perfectly OK 21-plate truck batteries, which he says should sustain 12 hours of standby power, even with the screen on). It is there to handle short power outages (<10 minutes) and then allow the machine to shut down cleanly.
There are two major types: