Single phase current is what you have in your house–the electricity comes in on a single wire, and it alternates (switches direction). If you were to actually look at the current you’d see it doesn’t just switch abruptly from one direction to the other, though, it follows a sine wave.
Three phase current is basically the same, but instead of having just a single wire, you have three of them, and the sine waves travelling through each are offset from each other so they come to their peaks at different times. It’s actually how power is generated in the first place, and it’s also used in most AC electric motors because it’s really easy to create a rotating magnetic field using it.
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