It makes a sort of helix and it’s weird.
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Funnily enough, Steve Mould has a (https://youtu.be/eOuai2p3qgw) on this exact topic. But here’s a short summary.
Water has surface tension. It tries to minimise the amount of surface area. For a column of water falling, that would be a cylinder. Imagine a thin slice of that column: it would be a circle. But we pee out of a slot shape. This means that that slice starts as an oval stretched front/back. Then, as it falls, surface tension causes it to pull in at the front/back and push out at the sides. It briefly forms a circle, but then momentum causes it to continue in those directions, instead forming an oval that’s stretched at the sides. Then, it pings back the other way and the cycle repeats as it falls. And the same happens for every other thin slice of that column.
All this together causes the whole stream to look a bit like a length of chain (not so much like a helix if you have a good look).
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