Practicers of meditation have known this for centuries. By purposely focusing on the center of a mandala, the eye movements slowly come to a stop and the visual imagery fades away. Try it!

I believe there's also been research showing that eye saccades significantly increase the effective resolution of the eyes over the physical resolution of the retina. I'm fairly certain there was some research done in making digital image sensors that "shake" to achieve the same resolution increase.

There have also been several studies showing that we briefly cease to perceive anything during the saccades. One experiment had people reading a document on a monitor with a sensor that detected the timing of their eye saccades. During a saccade, the computer would switch words in the sentences the person was reading. The changes were never perceived by the reader, even though people looking over their shoulder (whose saccades were not synchronized with the changes) immediately detected the changes and realized the content and meaning of the document was changing in real time.

It makes sense that apparent resolution could be increased by moving the sensor or the objects in view because transistions could be detected.

A good analogy would be optical encoders. You can either count the full pulses or you can use software and/or hardware to detect the edges to multiply the resolution.

Hmmm, wonder what mutation is responsible for this in humans :)

Why do I suspect that's not a serious question. :-) My guess is that no mutation was necessary. I've read that eye saccades match waveforms that inherently occur in the biological neural nets that control the eye. So it's probably far more likely that a control system taking advantage of such movements would occur than the other way around. Just a guess though. Eye movements have been heavily studied for years, so I wouldn't be surprised if your answer is out there. The eyes in general are wonderfully useful examples of evolution because they're apparently so trivial to evolve and yet so handy to have. A quick google turned up a couple of essays on the subject that might point in the right direction:

Where d'you get those peepers?, Richard Dawkins

Darwin will rest easier thanks to flies with eyes on their wings, Elizabeth Finkel

I find it difficult to accept the term 'trivial' in any discussion about the complexity of a cell, much less the incredible subsystems of, and the eye itself.

I'm glad we can agree on 'handy' though :)

I had a girlfriend that worked for a lady who's eyes constantly jiggled! It was really freaky to talk to this boss lady because you couldn't help but notice her eyes going back and forth as she looked at you. Silly me, young as I was, I asked her how did she do that. To which she replied, "Do what?" "Uh, nevermind," I said. Perhaps she was high, or at least had a higher resolution of vision? Or maybe she's really a mutant?

When thinking about human stereo vision I reasoned that these small involuntary movements could help us to recognize the curvature of surfaces . As the eye moves, waves of correlation could pass through part of the brain. Comparison of the speed of these correlation waves would allow regions of the brain to calculate the curvature of a surface directly.

Thats just my own rambling train of thought though... I came up with that thought when I realized how good my eyes were at noticing small depth changes in a sidewalks texture and trying to come up with an explanation.