Stare at the center of the rotating spiral for about 20 seconds, then look elsewhere. You will notice that whatever you look at now appears swirling. Don't worry, it won't stick ;-), this sensation will go away after a few seconds.
You can start/stop and adjust the speeds of the 3 parts of the spiral with the controls at top right.
Gazing at the spiral for a longer time will increase the duration of the aftereffect, leveling out at ≈ 30 s. Holding the gaze steady at the center (don't over-concentrate, "let it hang”) also increases the effect.
The basic phenomeon is called "motion aftereffect”, which I have described in more detail here. I added the present page because many observers find this three-part spiral more compelling. The spiralling aftereffect was first described by Joseph Plateau (1801–1883) in 1849. The variation into 3 regions was, to my knowledge, developed by the magician Jerry Andrus.
Plateau J (1849) Bull Acad Roy Sci B A Belg 16:254–260
Wade NJ, Heller D (2003) Visual motion illusions, eye movements, and the search for objectivity. J Hist Neurosci 12:376–395