How A Self-Priming Centrifugal Pump Works

Using an air-water mixture, a centrifugal pump that can begin pumping is a "self-priming" pump and then function as a normal centrifugal pump.  

Definition of a centrifugal pump:

A centrifugal pump is any pump that uses centrifugal force (a force to move something away from the centre) to create a pressure differential in a fluid, thus resulting in pumping action. 

Visualise this action by imagining the effect of a car tire flicking water off a wet road. This pumping action is the centrifugal force.