The main goal of a wing is to create thrust with, an amount of force that is equal to the weight of the aircraft but pointing in the opposite direction, so the wing can lift the aircraft's weight. A wing flying through the air, creates low air pressure above the wing and high pressure under the wing.
I'd rather drop the word "lift" because some people think it's something other than thrust. Interesting is the fact that most aircraft's thrusters (propellers, jets) don't produce enough force to lift the aircraft up vertical. These thrusters instead transform their energy into the aircraft's speed, relative to the ambient air. Efficient thrust comes from accelerating a great weight of air, just a little bit. A wing can accelerate a lot of airmass downwards, but a propeller can't accelerate as much weight. So, the energy of an aircraft's propeller is mainly transformed into in:
- Driving the wings through the air. (Gearing down from high speed low weight, to low speed high weight, which is a more energy efficient way of producing thrust).
- Air resistance of the other aircraft parts.
The rotary wings of a helicopter are something inbetween: a really big propeller, or a very small wing.
Let's start at the beginning.
Imagine a wing with an absolute flat and extremely thin airfoil, having a speed of say 200 km/h relative to the ambient air, and zero angle of attack. This situation produces no upwards thrust obviously. There is something happening though: the air and the surface interact where they touch; the boundary layer. The air and the surface kind of stick together on an atomic level (nanoscale). This causes drag on both the airfoil and the air. The air, bying a fluid, first develops layers of laminair flow with different speed on different distances from the surface. But then the air becomes turbulent, having random motions (well, not really random, we just can't see the logic).
Now, if the angle of attack is made positive, the air in front & under the wing has a conflict with the wing. They're on the same path, but as they can't be at the same place at the same time. The wing is solid and the air is a fluid mixture of gasses, so as these two each try to push the other away, the air will become compressed but the solid surface will not (not noticable). Air will flow away from this higher pressure area to any area of less pressure, which in this case is mainly downwards. The wing is pushed mainly upwards by the compressed air.
At the same time, the wing leaves a void behind, a vacuum space on top & behind the wing's airfoil. Vacuum space has an air pressure of zero point nothing. The ambient air has a pressure of about 1 KG per square centimeters, that is about 10.000 KG per square meter! Air still flows from a higher pressure area to a lower pressure area, so it will travel to this vacuum with great acceleration! The information about airpressure travels through the air with the speed of sound, about 340 M/S. Air is pretty light, but doesn't weigh nothing. Air weighs about 1,2 KG per cubic meter. So the vacuum isn't instantaneously filled, so the pressure will stay low on top of the wing.
Both processes are continuesly, so this wing with keep having higher pressure on the bottom and lower pressure on top.
An extremely thin wing isn't practical because a wing needs structual support, and there should be room in the wing for controls and such. Placing the support at the front bottom is actually the only option, because it doesn't enlarge the frontal area there. The high pressure story is lost by this. Making the support thinner can bring back some of the high pressure.
Air flows. It doesn't flow cornerwise. It, like all mass, doesn't want to accelerate, so if it has to, it accelerates as slowly as possible. The shape of the airfoil should be nice to the air. If the airfoil is hard on the air, it will resist, and that we call "air resistance".
The result of these few logic steps brought us a typical airfoil shape as result.

An airfoil, with illustrated air parcels and pressure areas around it.
What a wing does to the ambient air
The air on top of a wing is accelerated downward and a bit backward.
The air on the bottom of a wing is accelerated downward and a bit forward.
Looking at it in a Newtonian way: the wing accelerates air-mass mainly downwards, this action force on the inertia of mass gives a reaction force upwards: lift. (Inertia = the slowness of mass, not wanting to accelerate)
Looking at it from an air-pressure point of view: a wing creates a continues implosion on top (low pressure), and with a higher than normal angle of attack it also creates a continues explosion on the bottom (high pressure).
At the leading edge (the front of an airfoil), the air has to move away and is therefore of higher presence. This pressure "information" is "communicated" forwards by a pressure wave traveling through the air with the speed of sound; about 340 m/s. When flying with an airspeed of 330 m/s, the pressure wave from the leading edge is traveling forward with only 10 m/s (relative to the wing). This causes an enormous build-up of pressure; nearing the sound-barrier. The leading edge of most aircraft is round because the angle of attack must vary. A razor sharp leading edge prevents most pressure build-up, but can only be used with one angle of attack. (a delta wing with a sharp leading edge can create vortex-lift, but that is an other story!).