Why is air accelerating over the wing surface?
The Abdullah's answer is correct to it's level of approximation, but I'd like to expand on why the pressure is reduced on the leeward side.
As the air encounters the leading edge, it is pushed out of the way. Due to first law of motion, it would like to continue moving outward from the wing and avoid the area just above the wing. But besides inertia, air also has viscosity, which prevents sharp changes in air velocity, so the incoming air trying to pass high above the wing drags the air near the wing along. But when the air just above the wing is pulled out aft, there is shortage of air just over the wing, which means low pressure.
This low pressure causes the air bend around the wing, and since it pulls air from all sides, accelerate as it enters the low pressure region over the leading edge and decelerate again as it leaves it over the trailing edge.
Without viscosity (e.g. in liquid helium) the pressure would not be reduced, because the oncoming fluid would just continue straight over the highest point and the area over the receding part of the upper surface would be filled with stagnant fluid moving with the wing. In fact that's exactly what happens in stall – as the curvature increases (due to higher angle of attack), at some point the viscosity is no longer enough to keep the air moving, the area over the wing gets filled with air just whirling around and not moving away, so there is no longer shortage of air, the sucking of oncoming air stops and the generated lift rapidly decreases ­– just the lower surface still generates some.