What you have in your house is nothing to do with the 3 phase high voltage power distribution system.
Out in the street somewhere there is a transformer that converts the voltage between two phases of the high voltage power supply to a centre-tapped 220 volt output from a single winding.
The opposite ends of this are out of phase with each other by 180 degrees. When one end swings positive relative to the centre tap, the other swings negative.
Other appliances and lighting in your house use the centre tap (as a neutral) and one of the outside legs (as an active) of this winding to get 110 volts.
This system is fairly unique to North America. Most other countries bring one of three phases or all three phases into the house at about 230 volts. High power (at about 400 volts) is available between the phases. Three phase motors are more efficient than single phase ones and self starting, too