Because optical illusions are a magician's stock-in-trade, we tend to think of them as kids' stuff. However, illusions can tell us a lot about how we see, giving clues about how our eyes work.
Let's start with the mechanics. We don't see just with our eyes, but with our brains. Our eyes are the mechanisms for picking up information on light, color and shape. Our brains translate that information as people, or paintings or books filled with text.
But sometimes, the translation doesn't come through.
For example, check out the video below. Bring it full screen if you can (it works even better in the dark) and stare at the green dot in the center. One or more of the yellow dots will blink off, then blink back on again. Sometimes all three will disappear, and sometimes just one will blink. You really have to focus on the center of the screen and the green dot to make it happen. Blinking or shifting your eyes will bring the yellow dots back into your field of vision.
So what's happening? No, the yellow dots aren't disappearing. Your eyes are picking up the same information the whole time you're looking at the video. What's preventing you from seeing the yellow dots is a neurological phenomena called "motion-induced blindness."
Unlike what many of us think of as blindness — a problem with the eye — motion-induced blindness or MIB occurs because of the way our brains process information. There's nothing wrong with your eyes.
As Yale researchers Joshua J. New and Brian J. Scholl wrote in a 2007 study on the subject, "In motion-induced blindness (MIB), a target stimulus may disappear and reappear from conscious awareness when it is presented along with a global motion pattern."
This probably happens in real-life situations too. How often objects disappear in a moving field (and for how long) depends on a number of factors, including the size of the object, if the objects are grouped together, and how the background pattern moves. But it seems to work in a wide variety of situations and experiments, as shown on this page.
Previous research has suggested that visual "hiccups" like this happen when visual attention is overloaded, but why it happens in these specific circumstances is still being studied. It may be that, as researchers New and Scholl discovered in a follow-up study in 2008, “rather than being a failure of visual processing, MIB may be a functional product of the visual system’s attempt to separate distal stimuli from artifacts of damage to the visual system itself.”
So this could be a way for the visual system to protect itself, but the researchers still have work to do to understand why.