For any machine or rotating electrical equipment, we require atleast two fluxes so that they could interact. But as the motor bears only one phase, two fluxes are not possible. Thus in order to obtain a second flux to be cut, we introduce phase shift (usually through condensers) of 90 degree(ideal). This new flux thus obtained interacts with the actual flux and then the motor starts to rotate.
If we need we could keep the capacitor connected for pf improvement or else the auxiliary winding could be removed by using centrifugal switches.