How does Bernoulli's principle affect an airplane?

It is what allows an airplane to fly at all.

Bernoulli's principle states that for a fluid moving around an object, less pressure (force) is exerted on the surface where the fluid is moving more rapidly than where it is moving more slowly. The shape of an airfoil (wing) is such that air must move more quickly over the top of the wing than across the bottom. This generates lift because the air under the wing pushes it up into the (lower pressure) air above it. For a suitable shape, the angle of attack can be zero, or even less than zero, and still generate lift, because it is not only the angle of the wing generating the lift.