This illusion is one of several effects in which a rigid object is shown moving behind small apertures. The object appears to change size or shape as it moves. In this case the apertures become progressively narrower and wider as a square rotates behind them, and the square appears to expand and contract rhythmically ('breathe').
The illusion exposes the properties of mid-level motion processes which attempt to draw inferences about the shape of moving surfaces by integrating information across large image areas. Synchronicity leads the visual system to assign the movement seen in different apertures to a single object. When the apertures are very narrow, the motion signals are predominantly along the aperture boundaries, leading to apparent object expansion and contraction. But when the apertures are wide the extended visible contours and corners are sufficient to code the motion of the object as rotational.
See:
Meyer, G. E., & Dougherty, T. J. (1990). Ambiguous fluidity and rigidity and diamonds that ooze. Perception, 19(4), 491-496.
Shiffrar, M., & Pavel, M. (1991). Percepts of rigid motion within and across apertures. Journal of Experimental Psychology: Human Perception and Performance; Journal of Experimental Psychology: Human Perception and Performance, 17(3), 749-761.