How do I explain what makes an airplane fly to a non-technical person?
The simplest explanation is the "hand out of the window" one:


  Hold your hand out of the window while in a moving car and hold your hand at an angle. It gets pushed upwards. Your hand represents the wing of an airplane. The plane's engine simply makes sure the "hand" keeps moving forward against the force of the wind.


Even a 4-year old understands the concept using this explanation.