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A three phase motor will run just fine when single phased IF:
1) It's already up to speed AND
2) The load is less than 1/3 of nameplate power.
The whole idea behind three phase power is that the motor has three sets of electromagnets connected to three phase power. Three phase power has three different phases - Phase 3 lags behind Phase 2 which lags behind Phase 1.
Phase 1 energizes electromagnet 1 and pulls the rotor toward electromagnet 1. Then Phase 1 turns off and Phase 2 turns on. Electromagnet 2 is rotated 60 degrees from electromagnet 1, so the rotor is pulled toward electromagnet 2. Repeat for Phase 3. Then the phases reverse polarity for the next half revolution. The rotor is continuously chasing next electromagnet.
In practice, the three phases have a sinusoidal waveform and overlap. An electrical engineer can explain all this better and more accurately.
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