When objects move through air, they must push the air particles out of the way, this is where air resistance comes from. The faster an object moves, the more air it needs to push out of the way every second of falling. This increases the magnitude of the air resistance. The diagram below shows this effect.

The ball on the right is falling faster so the red area that it covers is bigger. This means it needs to push more air out of the way, and so the air resistance is larger.