This is because, as the source of light is moving across your field of vision, it is exciting different areas of your retina. With a stationary light source, persistence of vision (POV) would make the light source appear continuous, uninterrupted, because the rods/cones do not have time to clear the signal. You can perceive the LED being switched on and off as POV does not come into play.
This must be what I experienced this weekend. I was trying to take a picture of some LED light fixtures and they were doing a number on my camera's sensors. Black bands that at certain angles would move across the screen even though the camera and the lights were stationary.
