A doorknob is considered a wheel and axle because it has a wheel portion, the knob, and an axle, the rod in the door, that turn on the same axis. In instances such as a doorknob, a wheel and axle can also be considered a type of lever.
One common conception of a wheel and axle is as a tool to reduce surface friction to easily roll an object from one place to another. This is the type of wheel-and-axle system used in cars and bicycles. Under this configuration, a force is applied to the object, and the comparatively reduced surface area of the wheel as well as the wheel's size compared to the axle make the object easier to move. A larger wheel generally makes an object easier to roll.
The wheel and axle can be used as a type of lever. A force applied to the outer rim of a wheel creates greater torque on the axle than the same force applied to an axle without a wheel. This is because the wheel functions as a lever to create a mechanical advantage. The larger the wheel, the larger the mechanical advantage, and the easier it is to turn the axle. This is the type of wheel-and-axle system that a doorknob creates.