Three Phase and Single Phase in Simple Terms

Electrical service is transmitted in the form of alternating current whose magnitude and direction reverse cyclically (60 times per second). That is, if you put a voltage meter on a single phase AC line, (and magically slowed it down so that you could see it) the voltage would peak in one direction and then reverse polarity sixty times per second.

Graph of single phase single pole current

Three phase service is just three single phase lines which are out of phase by one third of a cycle so that the individual voltages peak one after another in sequence.
Single phase current can be converted to three phase using a rotary phase converter, but there is often a significant loss of efficiency and the possibility of dammage or accelerated wear to equipment involved . Nevertheless, used three phase shop equipment often sells for extremely attractive prices, and the determined do it yourselfer can actually convert a three phase induction motor into a rotary phase converter pretty easily.

Graph of three phase current

 Notice that single phase two pole current - 220 or 240 volt usually controlled by double pole breakers in the service panel, is single phase because the negative voltage peak of one conductor coincides with the positive voltage peak carried by the other conductor.

Graph of single phase two pole current

 The main power transmission trunk lines that originate at power plants and substations are three phase, but branches off of the main lines often consist of only one conductor carrying single phase power. This is why power in rural areas is most likely to be limited to single phase, and industrial customers tend to be clustered around the availability of three phase power
The main reason that industrial customers use three phase power is that high powered electrical induction motors that run on three phase are very simple in design and last for a long time and are cheaper to produce than single phase electrical motors. Of course large commercial consumers may also use three phase service simply because of very large energy requirements.