This describes it far better than I could. ..
A split-phase electricity distribution system is a 3-wire single-phase distribution system, commonly used in North America for single-family residential and light commercial (up to about 100 kVA) applications. It is the AC equivalent of the original Edison 3-wire direct current system. Its primary advantage is that it saves conductor material over a single ended single phase system while only requiring single phase on the supply side of the distribution transformer. Since there are two live conductors in the system, it is sometimes incorrectly referred to as "two-phase". The two live or "hot" conductors waveforms are offset by a half-cycle, or 180 degrees offset, when measured against the neutral wire. To avoid confusion with split-phase motor start applications, it is appropriate to call this power distribution system a 3-wire, single-phase, mid-point neutral system.
In North America, the high-leg delta system allows single-phase 120 V loads and 240 V three-phase loads both to be served by the same three-phase, four-wire distribution system.
A transformer supplying a 3-wire distribution system has a single-phase input (primary) winding. The output (secondary) winding is center-tapped and the center tap connected to a grounded neutral. This 3-wire system is common in countries with a standard phase-neutral voltage of 120 V. In this case, the transformer voltage is 120 V on either side of the center tap, giving 240 V between the two live conductors, shown as V1 and V2 in Fig. 1. The two outputs are properly called "legs", not "phases".
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In Australia and New Zealand, remote loads are connected to the grid using SWER (Single Wire Earth Return) transmission lines (it is cheaper to run one wire than two). The primary of the transformer is connected between the high voltage line and earth, the secondary is a 3-wire single-phase system as described here, the secondary voltage being 230/460 V. Single phase loads are split between the two circuits. Hot water services use both circuits.
In countries whose standard phase to neutral voltage is 120 V, lighting and small appliances are connected between a live wire and the neutral. Large appliances, such as cooking equipment, space heating, water pumps, clothes dryers, and air conditioners are connected across the two live conductors and operate at 240 V, requiring less current and smaller conductors than would be needed if the appliances were designed for 120 V operation.
No individual conductor will be at more than 120 V potential with respect to ground (earth), reducing the earth fault current when compared to a 240 V, 2-wire system that has one leg (the neutral) earthed.
It does explain the difficulties with importing into the US since things is 230v baseline.