Cufflinks are items of male jewelry that are used in dressy shirts in lieu of buttons on the sleeves. A relatively recent innovation in male attire, cufflinks supplanted the old-fashioned tie which previously held men's shirt sleeves closed at the wrist, and were themselves supplanted by buttoning cuffs.
Cufflinks are still in vogue for formal wear, and require that the dress shirt be made with French cuffs. These are sleeve ends that are longer than the arm to the wrist, so that uncuffed, they fall to the knuckles. The sleeve is folded back one turn, and then clipped together with the cufflinks through the 'buttonholes,' a misnomer here, since there is one hole on each side and no button.
While buttoned sleeves are made to overlap in a spiral, cuffed sleeves are intended to be closed with the two sides together so that the sleeve end comes to a stylist point. Cufflinks can have motifs on both, or only one side, with the undecorated side being the mechanism -- usually a bar that rotates horizontally to prevent the cufflink from slipping back through the buttonholes. If wearing cufflinks with only one decorated side, such as a jewel or a monogram, the decorated side goes on the outside. That is, with your arms at your sides, the decorated side of the cufflink should be visible and the mechanism side hidden.
When selecting dress wear, it's important that the dress jacket be tailored with French cuffs in mind, if you are planning to wear a formal shirt with cufflinks. The sleeve of the jacket must be roomy enough that the cuffed sleeve isn't squashed flat. Otherwise, when you 'shoot your cuffs' -- the male preening gesture that aligns jacket sleeves and shirt sleeves -- you run the risk that your cuffs will emerge from the sleeves and the sleeves be too narrow for them to retreat back inside.
Cufflinks can be obtained in a variety of materials, styles and prices. While jewels on cufflinks are unexceptionable, very large diamonds might present an organized-crime look to the ensemble. Monograms are always correct. Fanciful cufflinks with emblems of a trade are always popular -- t-squares for architects, for example. Organizations, lodges and fraternities will often supply their members with cufflinks indicative of their affiliation. And of course, cufflinks with the Presidential seal are always status symbols.