A purely 240V circuit consists of two wires, which I've labeled Hot+ and Hot-. These two wires will have the same voltage magnitude, but at any point in time they will be of the opposite sign: When Hot+ is +120V, Hot- will be -120V. So the difference between the two is 240V.
Many devices are designed to work when connected just to 240V.Water Heaters, some air conditioners, some motors, etc. The wiring for such a "pure" 240V device will consist of two insulated wires, (Hot+ and Hot-),plus ground. There is no need for a neutral conductor, because whatever current flows in to the device via Hot+ will flow out via Hot-.
However, many appliances (and other devices) need both 240V and 120V. The 120V part of the device is connected between one of the Hots and a third conductor, the neutral. The 240V current will come in via Hot+ and exit via Hot-; the 120V current will come in via Hot+ but exit via the Neutral conductor.
(We can't use the Ground conductor for the return 120V current, since the ground is to be used for safety purposes only.)
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