Without the horse tail in place, the right and left sides of the rectangle will look different. Actually, they’re the same, but graduated in color. At the right edge, both rectangles are dark gray. Both become lighter toward the left. Where the rectangles meet, the darkest part of one rectangle contrasts sharply with the lightest part of the other, so you see a distinct edge. When the edge is covered, however, the two regions look the same uniform shade of gray (in general, your brain ignores slight gradations in gray levels).
It’s often difficult to distinguish between different shades of gray or shades of the same color when no sharp edge divides them. This is true even though a sensitive light meter would show that the different shades are reflecting different amounts of light to your eyes. It's not that your eyes lack the necessary sensitivity to detect the difference: with an edge between the two shades, the difference is obvious.
Your eye-brain system, however, condenses the information it obtains from more than a hundred million light-detecting rods and cones in the retina in order to send the information to over a million neurons to your brain. Your eye-brain system enhances the ratio of reflected light at edges. If one region of the retina is stimulated by light, lateral connections turn down the sensitivity of adjacent regions. This effect is called lateral inhibition. Conversely, if one region is in the dark, the sensitivity of adjacent regions is increased. This means that a dark region next to a light region looks even darker, and vice versa. As a result, your visual system is most sensitive to changes in brightness and color.
When the horse tail is absent and the normal boundary is visible, lateral inhibition enhances the contrast between the two shades of gray. The bright side appears brighter and the dark side darker. When the tail is in place, the boundary between the two different grays is spread apart across the retina so that it no longer falls on adjacent regions. Lateral inhibition then does not help distinguish between the different shades, and the eye-brain system judges them to be the same.