The Lilac Chaser is a visual illusion that actually consists of multiple optical effects. If you stare directly at the + in the center of the image, you will quickly notice that the purple discs will slowly disappear. You should also notice that a single green disc rotating around in a circle will suddenly appear caused by an afterimage effect.
This illusion was discovered by Jeremy Hinton around 2005. He stumbled upon the illusion while researching visual motion stimuli.