power is the method by which electrical power is generated, transmitted, and in some cases, consumed.
As you may already know, alternating current reverses polarity 60 or 50 times a second, depending on where you are. If you plot the voltage as Y on a graph with the time being X, you will get a sine wave. Three phase power can be thought of as three different sine waves which are 120 degrees apart.
Three phase power is used because it is more efficient to generate and use. For instance, let's say you have a generator that is putting out single-phase power, that is, one waveform. For every revolution of the generator's rotor, you will only be converting mechanical energy into electrical energy part-time, IE, when the output voltage is non-zero. The waveform will only reach its peaks every 1/120th of a second; the rest of the time, output power will be sub-optimal, and the turbine won't be evenly loaded.
Enter three-phase power. If you look at a plot of all three phases, you will notice that at any given moment in time, one of the phases is nearing a peak. This means that a three phase generator will be converting mechanical energy into electrical output nearly 100% of the time, resulting in much more even loading of the turbine and better use of the generator's capability.
The same holds true for electric motors. A single-phase motor's power output varies wildly 120 times a second. This results in a lot of vibration. A three phase motor will run much smoother since almost full power is available from at least one phase most of the time.
Three phase power can be wired in one of two ways. There's WYE, in which the phases are connected in a "Y" shape with common neutral, and Delta, where the phases are connected in series, like a triangle. Delta arrangements are common in high voltage power line distribution, whereas WYE is more common in low voltage distribution within a building.
Residential and small business electrical installations are generally single-phase; one of the three phases on the utility poles is tapped by a transformer, providing a single low voltage phase. Three phase power is rarely needed outside industry because it's not cost-effective for small loads.