There are two sides to the gizmo shown in the photo above - the front side has no "spot." When you hold that side up and rotate it rapidly in about an 8-inch diameter, spots similar to the one in the photograph "appear" due to "rinsing" by the eye.
The gray circles appear due to the process of "rinsing," which is a type of stroboscopic effect between the pinwheel and your eye motions. These things with a large number of different designs are used as research tools in investigating eye motions. What you see depends on the design, how fast you move it in circles, and your eye motions. Clever researchers have produced big books of hundreds of these designs for which the particular pattern seen depends on the nature of the eye motions, allowing them to deduce information about eye motions.
SUGGESTIONS: With a bit of practice you can start rotating it with the non-spot side up, then flip it after the spots start to appear, magically creating a spot where none previously existed. This can be an amusing magic trick, but be sure to explain the real mechanism afterwards!
Electronic versions of the pinwheel blanks and instructions available upon request; email lecdemhelp at physics.