I was once asked this question a few years ago and I replyed with the usual answers. After thinking about it a bit more and read further (including a running debate in New Scientist) I realised that there is a major failing in the standard answers, as regards giving a basic understanding what is actually going on.
Firstly, except for some military planes, no plane has the power to fly by engine power alone.
Simple test, take a 747, put it on its a*s*, firewall the throttles ... nothing happens.
So where is the free energy coming from?
At its most basic it is N3, but not the way as usually described. For the simplest explenation it is actually better to think of air as particles.
Each particle has mass and hence momentum (due to temperature [=energy]every particle is moving) and every particle repels each other (think of springs coupling every particle).
What happens with a plane (or a skipping stone on water, or a neutrally ballested submarine) is when it moves the wing represents an immovable surface (as it is not a fluid). As it moves air particles bounce off the wing, but they compress against other particles, which push back. Also there is a second effect because of resistance because they have momentum (think of snooker balls).
If the wing was totally flat relative to the air particles and a perfectly even shape then all the forces would balance out, the momentum transfer and the spring forces.
But if the wing is angled (I wont go into shapes at this level of explanation) the forces become uneven.
If you are a Formula 1 car you want the forces downwards, to hold on the road, if you are a plane you want the forces upwards, to lift you into the air.
Now these forces are quite small and evenly balanced at sea level and no air speed. But think of a hurricane (say 100kph+). The momentum and spring reaction from each air molecule becomes large. If you are standing in a hurricane at 200kph you (or your car or house) will fly! In this case the energy gap comes from the sun (somewhere out in the ocean)
The inverse happens with a plane. You go fast (the energy from fossel fuels) and you close the energy gap and (with the right angle of wing to create unbalanced forces ) you lift.
Summarising: You get free energy from the momentum and repulsive forces of each air molecule. Normally these are evenly balanced. But, if you add energy (speed) and unbalance these forces they will lift you, even though the energy you expend in going fast is not enough to overcome gravity. Basically you get free energy from the atmosphere.
Simple test. You are in on a planet in a vacuum. You go very fast .. what happens?