The following are the main advantages of 3 phase system over single phase system.
In single phase circuits, the power delivered is pulsating. Even when the voltage and current are in phase. The power in zero twice in each cycle. Whereas in polyphase system power delivered is almost constant when the load are balanced.
The rating of 3 phase machine is nearly 1.5 times the rating of a single phase machine to the same size.
To transmit same amount of a power over a fixed distance at a given voltage, 3 phase system requires only 75% of the weight of conducting material of that required by single phase system.
3 phase induction motor is self starting whereas single phase is not self starting.