The whole system of motion is much like a wave in the water. The circulation of air around a wing is like a wave that moves with it, similar to the wake that moves along with a boat.
Air is pushed forward under the wing and accelerated backward over the wing (black arrows). Also, air tries to move from high to low pressure. By the time the wing arrives, the air has established a pretty good up-wash ahead of the wing and, by the time the wing has passed, all the air is lower than it was before. Each particle of air is moved slightly up and down. The square at the right side shows the vertical pattern of one single particle above the wing, as well as one below the wing, at the time the wing passes. The particles in the air mass are all bumping into each other, and each is affected by the ones next to it. The combination of these particles pattern and movements is called circulation.
This downward movement is the primary mechanism of lift, since the lift of a wing is proportional to the change in momentum of the air it is diverting down.