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There's an article linked in the description which goes into it, although it stops short of a full explanation.

In summary - starfish have many many feet, but no brain controlling them. The feet are all semi independent, and make their own decisions on where to go based on sensors on the feet themselves. So when a starfish starts moving, at first all the feet are sort of doing their own thing, but it's easier for them to move along with other feet around them, so they begin to synchronise spontaneously like in the video.