Three-phase power is designed especially for large electrical loads where the total electrical load is divided among the three separate phases. As a result, the wire and transformers will be less expensive than if these large loads were carried on a single-phase system.
Three phase generators usually have three separate windings, each producing its own separate single-phase voltage. Since these windings are staggered around the generator circumference, each of the single-phase voltages is "out of phase" with one another. That is, each of the three reaches the maximum and minimum points in the AC cycle at different times.
Electricity is generated at power companies in these three phases. But, if three phase power is better than single phase, why not four, five or six phase? Theoretically, these would be even better, but equipment manufacturer's would have to build motors to use it, and that just wouldn't be cost effective given the installed base of three phase equipment that must continue to be powered.
The word phase is often abbreviated using the Greek letter "phi" and is written as a zero with a slash mark through it.