Scientists have tried to figure out how a plane flies and although they don't agree on exactly how it does, they have a good idea. The four forces acting on a plane, Newton's Third Law, and Bernoulli's Principle all are used to explain how a plane flies. Lift, thrust, drag, and gravity are the four forces acting on a plane. Drag and gravity both act against the plane. Drag is something that obstructs the airflow, slowing down or hindering the way an aircraft moves. Gravity, as you know, pulls down on the airplane.
The lift and thrust have to be able to accelerate the plane through the air. If throwing a paper airplane, the persons arm is what gives it thrust. The angle at which the wings are at is what gives it the lift it needs to fly. All four forces have to be equally balanced in order for it to fly.
Daniel Bernoulli's Principle states that if a fluid (air) moves faster over a surface, then the static pressure decreases. This works for an airplane also. So when the air moves over the top of the airfoil, which is longer than the bottom route, it has to go faster than the air underneath in order to meet at the end at the same time. The pressure decreases above the wing and the higher pressure below the wing pushes the wing upward, creating lift. Another theory on how flight is possible is Newton's Third Law.
This states that for every action there is an equal and opposite reaction. This works to make a plane fly because the plane pushes down on the air ans the air pushes up on the wing, making the plane fly. With Newton's Third Law, Bernoulli's Principle, and the four forces acting together, planes are able to fly for hours with many passengers. But, still, no one really knows why..