In fluid dynamics, there's this principle called Bernoulli's principle. Basically, it states that the pressure a fluid exerts on a body is inversely proportional to its velocity. In other words, as velocity goes up, pressure goes down.
Now, switch gears for a moment and imagine a wide, slow moving river that suddenly and quickly narrows. What happens? The water moves faster right? This is the same concept being applied to a plane wing. Think of a wing cross-section. It’s kind of flat on the bottom, and it grows fat on the top. This expansion on top juts into the air stream and effectively narrows it.
Here's the neat part. The air on top of the wing is now moving faster than on the bottom. With knowledge of Bernoulli's principle under our belt, we know that the pressure drops when the air speeds up. There’s now a different pressure on the top of the wing than what’s on the bottom, and we've just created the pressure difference we call lift! Using some nifty mathematics, we can determine the amount of lift from two full-sized wings, and when the lift is equal to the weight of the plane, the plane will fly level. Flying out of an airport, you might’ve noticed your plane tilting up. By increasing the plane’s angle of attack (slowing the air flow over the top of the wing further), we can increase lift even more, making the plane go up. Descent is slightly more complicated. But in short, the pilot slows down the plane and Bernoulli’s principle takes over, dictating that a slower speed means less of a pressure difference across the wing’s cross-section, and the plane goes down. Cool huh?