Eccentric Eyeballs
Think of the eyeball as being positioned more or less "eccentrically." When the chin and center line are aligned and the eyes are simply resting, faced forward, that's zero eccentricity. Now, if you dart your eyes to the side, the eyeballs become eccentric—you've oriented your eyes, say, to the left, so that you can apply the center back of your eyeball—the cone-rich part, the precise, critical, vigilant part—to the left. That's not peripheral vision. That's foveating to the side. (Yes, foveating is a real word.)