The reason the air moves faster is rather complicated. Basically, though, there is one important feature of an airfoil that enables this: the sharp trailing edge. Imagine you have a circle moving through the air. You will have a stagnation point at the front and back where the air slows to zero velocity and attaches to or leaves the surface respectively. Now, start squishing that circle into an ellipse and you will start to have two pointier regions. If the ellipse is still pointed so that its long axis is aligned with the flow, the stagnation points will still be on those tips.
So, now you have to think, if Newton's laws imply that air must be deflected downward in order for the plane to be pushed up, then how do we go about accomplishing that? The idea then is to turn the ellipse slightly so that it acts sort of like sticking your hand out the window and exposing a bit of the long side to the oncoming flow. We call this angle it makes the angle of attack. As it turns out, though, in an inviscid sense and also a viscous sense for large enough tip radius, even at angle of attack, the flow will just turn around the small tips and your stagnation points will still be at the front and the back and will not be deflected downward at all. This is where the sharp trailing edge comes into play. In an inviscid sense, to navigate a sharp trailing edge, the velocity would have to go to infinity, which is impossible (or near infinity, as nothing is perfectly sharp). Instead, viscosity ensures that at the sharp trailing edge, the flow simply leaves the surface there. Basically, if you take your ellipse and continue to flatten it a bit and then squish the trailing edge into a point, you are enforcing the location of that rear stagnation point. Now when you put that shape at an angle of attack, you are deflecting the air nearby downward.
So what does this have to do with the speeds and pressures on the surfaces? You can look at it a few ways. Either you can say that Newton's laws show that there should now be an upward force, meaning there must be a pressure differential, meaning there must be a speed differential. Otherwise, you can say that if you look at the actual equations that fully describe continuum fluid motion, the Navier-Stokes equations, they will predict a faster flow over the top as a result of that geometry. In fact, you don't even have to artificially set the trailing edge as the rear stagnation point, as the Navier-Stokes equations sort that out for you since they include viscosity. In practice, it is also very common to simplify that problem and treat the flow without viscosity and just mathematically set that trailing edge as the stagnation point, and then even much simpler equations can get a pretty close answer.
So then, the bottom line is that you can look at it one of two ways:
- The sharp trailing edge allows the airfoil to deflect the flow, and Newton's laws require that there is a pressure differential and therefore a velocity differential. This won't help you calculate the actual values of the pressures and velocities at every point, but it should be rather intuitive in helping you reason out why there must be a pressure and velocity difference.
- With a sharp trailing edge, the more complete equations of motion (and, of course, nature itself) show that the velocity must be moving much more quickly over the top of the airfoil, thereby signalling a pressure difference.
How you prefer to look at it depends on what helps convince you of what is going on and just how in-depth you are trying to get here.
