A cufflink fastens a shirt by sliding through holes on either side of the cuff opening, then swinging into a locked or fixed position to hold the sides together. These are fastened by setting the toggle in its closed position so that there is a straight post descending from the underside of the head.
The most common cufflink consists of a large head or “insert member” with a decorative front face, a post that extends from the back of the head, and a hinged toggle that swings out from the post to fasten the link.
The post slides through the holes on both sides of the cuffs, and then the toggle is swung outward to prevent the post from sliding back out.
That holds the cufflink in place, with the front face of the insert member placed decoratively atop the buttonholes.