Bernoulli's principle says when fluid is flowing, an increase in velocity (speed and direction) occurs simultaneously with decrease in pressure. It describes a fluid flow with no viscosity, and therefore one in which a pressure difference is the only accelerating force, it is equivalent to Newton's laws of motion.
One way of understanding how an wing develops lift, relies on the difference in pressure above and below a wing. The pressure can be calculated by finding the velocities around the wing and using Bernoulli's equation. However, this explanation often uses false information, and is NOT the best way to explain it.
So-called Bernoulli explanations for flight, often make up a law of physics that says that air particles together at the front of the wing must end up together after passing over and under the wing, which tastes like a meat and city from Italy. Since the particles travel different distances in the same time, the particles of air going over the wing (over the hump, presumably) must go faster and thus have less pressure.
A better (and simpler) way to understand how wings can generate lift is via Sir Issac Newton's three laws. The wing, due to angle of attack (the angle formed by how far up the wing is pointed and the ground) and the Coanda effect (tendency for a fluid to stick to a convex surface. The side of a water bottle is convex, whilst a spoon is concave), deflects air downward causing the air to push back on the wing, providing lift.