How Does Power Get Split Into Phases?

Three phase power comes from the utility plant where it is generated by three separate coils on the generators themselves tapped off 120 degrees to each other.  By the time they get to a service outlet they have been upped and back downed to 120 volts (or so) with respect to ground and because of their phase difference of 120 degrees they are 208 volts apart between any two of the three phases.

Single phase power gets its name because it comes from just one of the three phases.  In the last stage of getting downed - often from 600 volts - it is transformed by a center tap transformer that pulls two hot taps and a neutral from the center of the coil.  The voltage of either tap with respect to the neutral is 120 volts (or so again) and the difference
between both hot taps is 240 since as a consequence of the center tap transformer...these two taps are 180 degrees out of phase.

It is customary in this country (United States) for residential customers to use single phase service and commercial customers to use three phase service.  Three phase power is much much better at running large horsepower motors, such as the type found in heating and cooling systems and manufacturing equipment.  The only stage equipment that actually use three phase are some chain motors (although many are wired for single phase, some are wired for 220 single phase and some others for 208) Dimming Racks and Audio Racks set up for three phase service in actuality distribute the three phases into three separate phases of 110 internally and function for all purposes as single phase 110.