The capacitor causes current that is not in phase with the supply current, therefore when applied to an aux winding strategically placed you get areas of the field that reach peak magnetism at different time than the main winding and tend to pull the rotor one direction or the other is about as basic of a description one can make here. This concept is for all single phase induction motors, some use capacitors others use other means to create the phase differential. The capacitor types are the ones that can develop more torque and are what is used for the higher capacity motors, most other methods (there is a "split phase" and "shaded pole" being the majority of other types) are only used on fractional HP motors