Well, explaining 3-phase power in a concise way is quite a task.
Basically, you have three "hot" wires supplying power. Are you familiar with the sinewave pattern of AC? Each hot wire is 120 degrees out of phase with the others, which in simple terms means that the peaks and nulls of the sinewaves on each phase don't coincide. That means that as well as there being voltage between any phase and neutral, there is also a voltage between phases. Thus you can obtain power by connecting either phase-to-neutral or phase-to-phase.
You can always work out the relationship between the voltages by multiplying or dividing by the square root of 3.
So a common 3-phase system specified as 120/208 volts will have 120V from any phase to neutral, but if you measure between any two phases you will get 208V. So a heater, blower motor, or whatever connected between two phases must be designed for the higher voltage.
The same relationship holds true for other 3-phase systems, such as your 277/480V system in America or the 240/415V we use here in England.
Perhaps a little easier to understand is the residential 3-wire system which has a neutral and two "hot" lines.
Technically, this is single-phase, but the lines are 180 degrees out of phase with each other, so when one is at its positive peak the other is at its negative peak. Thus you can get 120V from either line to neutral for normal lights & outlets, but 240V by connecting between the two hot lines. Hence the 120/240V specification for residential services.
That's all pretty simplified, but I hope it helps.
[This message has been edited by pauluk (edited 11-17-2001).]