The textbook definition would be something like this:
A phase is the factional part of the period of a sinusoidal wave, usually expressed in electrical degrees.
A single-phase circuit is an alternating-current using only one, sine wave type, current flow.
A three-phase circuit consists of three different sine wave current flows, different in phase by 120 degrees from each other.
A more practical definition:
Single phase: a circuit that consists of three wires – live, neutral, and ground (earth). The main breaker in a single phase system is a single pole breaker, resembling the others in the panel, only with a higher capacity.
Three phase: a circuit where the main breaker switches off three poles. For most home owners this is the equivalent of having 3 separate main breakers that are divided among the circuits of the home. There are 5 wires that normally constitute a three phase line, although in many homes the three phases simply supply the main and sub panels, but continue throughout most of the home as single phase lines. In most homes there are not many devices that run on three phase electricity. However, examples may include a three phase central air conditioner, a three phase oven, a 3 phase swimming pool pump, or a large 3 phase hot water boiler.
FAQs - Electrical Wiring