Single phase and three phase are two forms of alternating current which involve a sinusoidally varying voltage or current.
The single phase is used in a place where less power is required and for running the small loads. The three phases are used in large industries, factories and in the manufacturing unit where a large amount of power is required.
Before we explain each of them individually we need to know what is the phase?
Consider the following figure below. It shows two sinusoidally varying quantity. As you can see the blue one and the red one has a definite angle difference. The red one starts from zero. But the blue starts a bit later. The angle difference between them is considered as the phase difference.
In sinusoidal functions or in waves “phase” has two different, but closely related, meanings. One is the initial angle of a sinusoidal function at its origin and is sometimes called phase offset or phase difference. Another usage is the fraction of the wave cycle that has elapsed relative to the origin.
Therefore if an electric power supply system consists of a single sinusoidally varying voltage it is termed as the single phase.
If a certain power supply system consists of three sinusoidally varying voltages with a phase difference of 120 degrees then it is called as three phase system.
As compared to a single-phase AC power supply that uses two conductors (phase and neutral), a three-phase supply with no neutral and the same phase-to-ground voltage and current capacity per phase can transmit three times as much power using just 1.5 times as many wires (i.e., three instead of two). Thus, the ratio of capacity to conductor material is doubled.