Almost all homes are connected to single-phase electricity. The single-phase that a home is connected to is just one of the three-phases that are generated by our big centralised generators. The electrical distribution system is almost always all three phase right up to the point where the lead-in cable comes into an individual house.
An individual house puts all of its load onto one of the phases, so different houses get connected to different phases to help balance the load. Over a small number of houses the load can still be very unbalanced, because different households will use different amounts of electricity at different times; however, when many houses are connected to different phases they tend to even out and balance the load.
To enable different houses to be connected to different phases, the three phases must be connected differently to the delta connection that originates with the generator. The change in connection is done in the last transformer in the distribution system. Instead of the three winding being connected end-to-end as they are in a delta connection, one end of each of the windings are connected together at a common point, leaving three separate connections in a star shape for connections to the loads.