I don't think it does relate to it. A circle of confusion is the area covered by the blurred image of a point object (say, a small bright light); something that would ideally be rendered as a sharp point in the image, but isn't, because it's out of focus. The diameter of such a blurred image is used to define where the depth of field starts and finishes, in a quantifiable way. You can say that an object is just in focus when the circle of confusion is (say) 0.1 mm across; that is, we get rid of subjectivity in whether the thing is sharp by defining this criterion.
Then for a given focus distance and aperture, there are near and far limits (in the object field) where a point source of light will give an image that size, and those are taken as the limits of the depth of field, given this value of the limiting circle of confusion (I forget, without looking it up, what the conventional value is; it isn't 0.1 mm). This ignores other factors, including how much you enlarge the image afterwards, and how close people will be to view the picture.