Are you talking about the "leftover" spots after you look away from the bright thing?

The technical term for this is an afterimage. It's mostly caused by your brain compensating for the bright stimulation of the light. Basically, your brain is looking for contrasts, and it assumes that most of your visual field "should" be at a similar brightness, so it adjusts very bright spots down in brightness in a way that lingers for a short time. (Another, smaller, contributor is that the cells in the retina - the light sensitive part of your eye - can only be stimulated so often, and a very bright light can easily saturate all of those cells so that they're effectively "disabled" for a few seconds.)