This image from ONERA, the French aerospace lab, shows a simulation of the wake of an aircraft, looking along the direction the aircraft is moving. The spirals of moving air are called wingtip vortices. To learn more, visit this animation from the Smithsonian Institution's How Things Fly.
Also, compare the image above with this photo (from PTG Issue 33, in the Archives) showing the pattern of smoke released behind the wingtip of a crop-duster. How well did the simulation model the crop-duster wake?
How Airplanes Fly: A Physical Description of Lift
Visit the Florida International University site How Airplanes Fly: A Physical Description of Lift to understand how the wing of an airplane produces lift. You'll see that the frequently-given explanation based on the Bernoulli principle is not correct.