When you think of sleep, you think of eyelids closing over your eyes. But fish have no eyelids, so they have nothing to close over their eyes. Yet fish DO sleep.
Most fish sleep by keeping very still in the water. In this way, their bodies rest, just as yours does while you are asleep. But when fish sleep, it is not the same deep, sound sleep that you are accustomed to, and the slightest ripple in the water will disturb them.