I think the easiest explanation to a lay person involves the observation that all surfaces in a moving fluid (e.g. air) produce lift--whether a flat plate, rotating cylinder, or extending your hand outside a car window. Airfoils are merely highly optimized shapes to reduce the (often significant) drag the lift-producing bodies have.

In an airplane, by reducing L/D enough you decrease the necessary power (which indirectly produces its lift) needed to overcome the combined weight of the aircraft (wings/body/powerplant) generated by gravity.