For practical purposes: A three fase system can carry three times the energy using only 1.5 as much wiring, so it saves cost on infrastructure.
In a 50 hz system, a one fase system completes a full sinus-curve 50 times a second, while a three fase system completes three times as many. So the power is «cleaner».
There are also many other advantages to a three fase system, but it is difficult to explain in simple terms.
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