Left: aerodynamics on. Right: aerodynamics off.
The above animation of two cloth sheets falling with and without aerodynamics pretty much sums up all aerodynamics are about: they allow your cloth to interact with the air around it, through the calculation of two forces for each particle: lift and drag.
Applying aerodynamics to your cloth is very straight forward: just enable it, and tweak the following parameters until you're satisfied with the results:
How much drag affects the cloth. Intuitively speaking, drag is the force that allows parachutes to work.
How much lift affects the cloth. Intuitively speaking, lift is the force that allows planes to fly.
Aerodynamic constraints by themselves will only simulate a static atmosphere around your cloth, but not around other actors like softbodies, fluid emitters or ropes. If you want to add directional wind you´ll have to use force zones. (Note that there's no need to have any wind for aerodynamics to take effect, as the relative velocity between the cloth and the wind is what counts: even if there's no wind, if the cloth is moving drag and lift forces will act upon it.)