DIAGNOSIS: Something is physically interfering with the rotation track or gears. This is almost always a foreign object—a bug, a clump of dust/dog hair, or a small toy—that got pulled into the base.
FIX: Unplug the fan immediately to prevent further damage. Tilt the fan back and look into the gap around the oscillation joint at the very bottom. Use a bright flashlight. You'll likely see the culprit. Use a can of compressed air (like for keyboards) to blow debris out from the gap. If you can see a specific item, try using tweezers or a thin, stiff piece of plastic to carefully extract it. After clearing it, manually rotate the fan head a few times by hand to ensure it moves smoothly before plugging back in.
IF THAT DIDN'T WORK: If the noise persists after a visual clear-out, the internal gear might have been damaged by the debris. A tooth could be chipped, causing a rhythmic click with each revolution. That's a deeper mechanical issue.
HEADS UP: This is why regular vacuuming around the fan base is a good idea. Letting dust bunnies build up is a surefire way to eventually hear this noise. Don't spray liquids into the gap trying to clean it.