The Bernouilli Effect
A wing is a curved airfoil. On most aircraft, the bottom of the airfoil is fairly flat, whereas the top of it is curved. Air flows over the top more quickly, which causes it to thin out. Because the air is thinner at the top of the airfoil, it creates a vacuum. The vacuum pulls up on the wing, generating lift and helping to keep the airplane in the sky.
The Coanda Effect
Many people explain airfoil in terms of the Bernouilli effect alone, but there are other forces at work which help to keep airplanes airborne. There is a principle of physics called the Coanda effect, which states that a jet of fluid will tend to follow a curved surface. If you want to observe this at home, go hold the back of the bowl of a spoon under the faucet. Water will run down the surface of the spoon rather than dripping straight down. This phenomenon plays a key roll in making planes fly.
Newton's Third Law and the Coanda Effect
The trailing edge of an airfoil curves downward. As the air flows over the wing, it angles downward off the wing, shooting down behind it. Newton's third law of thermodynamics states that for every action, there is an equal and opposite reaction. For example, if you put a glass on the table, the weight of the glass pushes down on the table and the table pushes back up on the glass with equal and opposite force, supporting it. Similarly, as the airfoil pushes air downwards, that air pushes the airfoil upwards. This, along with the Benouilli Effect, keeps the airplane airborne.