There is nothing magical about three-phase power. It is simply three single phases synchronized and offset by?

Question

Why three phases? Why not one or two or four?

Answer 1

Very good question. Simple question but tough to explain. Let me try put in simple words. The electricity is generated by rotating rotor inside a stator. This is tapped to create three parts at 120 degrees by dividing the stator windings. Two or four phases might create (forming couple) equal and opposite forces at 180 degrees causing stalling problems.
This can be better understood in case of single phase motor. Single phase motors work on single phase power but the same phase is divided into two by using one capacitor in one line. But in case of failure of capacitor the motor does not rotate and sometimes rotates in clockwise or anti clockwise arbitrarily. This is because there is equal and opposite force of rotation on rotor by stator windings.
Three phases will never create opposite forces as they are at 120 degrees apart.

Answer 2

3 phases give maximum torque, 120 degrees apart, with only 3 wires.
One phase is common and used a lot, 4 phase would need an extra wire and not give substantially enough advantage over 3.