Relevance to this thread - none whatsoever. In fact this might get moved by the moderator, but until then...
APU stands for Auxilliary Power Unit. Very simply, an APU is a small engine that doesn't fly the aircraft, but can run a generator, air cycle machine, and suchlike.
Big jets with big engines have APU's because they can't start their own engines without them. They start the APU first (generally using an ordinary battery and starter motor) and then use the APU output (either compressed air, or electricity, or whatever) to start the main engines.
Smaller jets have smaller engines, and can therefore start an engine from their own battery (the second engine is then usually started from the output of the first). Smaller jets therefore don't need APU's.
If you were designing an aircraft you would only generally include an APU if you really had to - they are expensive, heavy, and represent another thing to go wrong. But APU's bestow considerable bragging rights on the flight crew, because if your aircraft has an APU, it must be BIG, and therefore your salary, car, and sexual appetite must also be enormous.
There is one other clever trick (and irritating source of noise polution) that APU equipped aircraft can do - the APU is generally sized with enough power output to run all the electrical system on the aircraft, so it is quite common for the crew to run the APU on the ground so that they can sit in the aircraft with all the lights on, drinking coffee, whilst waiting for the passengers. The primary purpose of this exercise is of course to emphasise to all the lesser crew on the ramp that this is a BIG aircraft with very important flight crew.
