APUs are used on the ground to provide power when the four main engines are shut down. Hence the name APU - Auxiliary Power Unit.
Don't know if you've worked on APU's, but the aircraft I have worked with can start and run APU's while the engines are running, to take the electrical load before the engines shut down, or in some cases as emergency electrical back up in flight... Just a flip of the switch to transfer Elect/Hyd control from normal to APU
Yes, there's a ground APU, too, used start the engines on the ground, keep the interior A/C running and to provide interior lighting while sitting at the gate. What I'm talking about is built into the tail of the airplane. It's an on board APU, a small gas turbine engine used to drive a generator which powers the aircraft's systems in flight. Take a look at the tail of a 747, 737, 757, 767 and other similar aircraft and you will see a "stove pipe" below the rudder. The intake is usually at the leading edge of the vertical fin or sometimes is fed through NACA ducting on the rear side of the fuselage. That's the APU. Do a Google search on "Boeing 747 APU" and you'll get a few hundred hits which describe what I'm talking about.