The explanation for this is essentially the same as the one given in this Snack. The wing collides with air, creating a region of high pressure in front of the wing. This high pressure produces drag, which is always associated with lift. The high-pressure air in front of the wing accelerates air over the curved surface of the wing. This air then flows downward behind the wing.
Airplanes fly because their wings throw air downward.
It is sometimes said that air must flow faster over the curved top surface of a wing than over the flat bottom. This is said to happen because the air has to meet up again at the far end of the wing, and since the air traveling over the curved path must travel farther, it must travel faster. This is not true. Two parcels of air that start together, then split to flow over different sides of a wing, do not, as a rule, rejoin at the far end of the wing.