You need at least two phases to get an induction motor started. Once it is started it can run on a single phase.
An induction machine starts by having a rotating magnetic field which induces current in the rotor. The current in the rotor iproduces a magnetic field which will chase the rotating field. In a single phase machine the field doesn't rotate but just switches back and forth. In a three phase machine, start ( and running) is acomplished by placing 3 sets of coils 120 ˚ apart and running them from a three phase voltage source. In a single phase machine you don't have the second voltage phase. By using a start capacitor and start winding, you can get some phase shift to get your motor started. Ususally there is a centrifical switch that opens the connection to the capacitor once the motor is spinning fast enough to keep going on its own. The start winding would overheat otherwise. Having a run capacitor also provides phase shift and will help get a little more power out .
