When air hits a flat panel at an angle, it gets deflected by the angle of the panel. Change the shape of the panel to optimize this and you get a wing.
Spin your wing in a circle, and it pushes air out one side. This is a fan, or a propeller. This generates a force on the wing in the opposite direction that it pushes the air.
Strap that to an airplane body and it pushes the airplane body forward.
Strap wings onto that, and the forward motion of the body + wings deflects air downward and thus pushes the body up.
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