A propeller works in a similar way that a screw works.
The blades of the propeller are an aerofoil, which generates an aerodynamic force as they spin, the same as any other aerofoil that is moving through the air. The blades of a propeller are slightly angled. As the blade rotates, air accelerates over the front surface, causing a reduced static pressure ahead of the blade. This results in a forward thrust, which pulls the aircraft along.
When the aircraft is stationary, the spinning propeller blades cause purely rotational velocity. As the aircraft moves forward in flight, the propeller produces both rotational and forward velocity. The combined vector of these forces is called the pitch, the angle of advance. As a result of this combined rotational and forward velocity, each propeller blade section follows a ‘corkscrew’ path through the air.
Different points along the blade will have an optimal angle to the relative airflow to operate efficiently at a given airspeed. Propellers are designed to have the most efficient angle of attack along the entire length. To achieve this, blades are designed with a twist, which reduces the blade angle from the centre to the tip.
Fixed-pitch propellers have only one forward velocity (airspeed) for a given rpm at which they will operate efficiently. Some propellers are designed with the ability for pilots to to ajust the pitch in flight, allowing the propeller to operate most efficiently over a wider range of airspeeds.