When you supply power to the the motor, the motor and the attached fan both spin. The centrifugal movement of the fan blades draws air in through the small round air inlets in the side casing of the hair dryer. The air is then blown down the barrel of the hair dryer. The small black fan sits atop the motor. The motor spins the fan.
Air is drawn in through the openings on the side of the hair dryer.
You'll see this referred to in the manual accompanying the hair dryer as high or low speed, because changing the airflow involves modulating the speed at which the motor is turning. This is accomplished very simply, by altering the current flowing through the part of the circuit feeding the motor. When the power supplied is low, the motor and thus the fan spin slowly. Less air is pushed through the hair dryer. With more power, the motor speeds up.