French cuff
Cuffs on a dress shirt which are folded back, and then closed via cuff links or silk knots, as opposed to with a built-in button. Cuff links and silk knots exist soley for shirts with french cuffs.
This is more formal than the typical cuffs on dress shirts which close via a built-in buttons (think your typical button-front shirt). Although more formal, french cuffs are optional and a matter of preference. If a standard suit (as opposed to a tuxedo) is formal enough for an occasion, then so are button-cuffs.
Alternatively, instead of cuff links, french cuffs can also be closed via the much less expensive, but just as formal and well-regarded, silk knots, sometimes also called monkey's fists. Silk knots tend to be more well known in Europe than in the United States.