I suppose 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.
Now let's have the more practical, "down to earth" definition - something that the average homeowner would at least have a chance of understanding:
Single...