Airplane APUs & GPUs - What are they? How do they work?

Have you ever been in a hot and stuffy airplane and you heard the pilot apologize because the APU wasn't working? Have you ever been onboard and all the lights went out for a few seconds?  So what is an APU? What is a GPU?  Captain Al Explains all about the Auxiliary Power Unit and the Ground Power Unit, how they differ and what happens when they don't work as intended.