Bernoulli's Principle explains how an airplane can stay aloft, even though it is heavier than the air. The upper part of the wing is more curved than the lower part, and this design is known as "air-foil" in industry. When airplane starts to move along the runway, the air through which it moves has to travel faster over the top surface of the wing to catch up with the air moving under the bottom surface. By Bernoulli's Principle, that means the pressure on the top of the wing is less than it is on the bottom, so there is a net upward force to lift up the airplane. In short, difference in pressure creates a lift force. When the plane is moving fast enough, the lift force exceeds the weight of the plane and the plane will lift off the ground and fly into the sky.
When the plane tries to land, it will slow down first, so the pressure difference exerted on the wing will gradually decrease, the lifting force gets much smaller and make it possible for the plane to go back to the land.