h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Information on sleeve buttons on men's suits. Men's coats, and their predecessors doublets were very often either open or able to be opened at the wrist. If you look at paintings and drawings of men's fashions from the 17th century onwards (and probably from earlier too), you will see that men's doublets/coats/jackets were often left open at the wrist, and it seems it was usually to display some rather decorative shirt details, either a fullness of very fine, and expensive, linen, or some even more expansive lace trim, either as a cuff or ruffle/frill (yes guys, frills!) So the wrist of the coat could be opened to reveal are gorgeous piece of shirt along with the expensive button closing, if it had a buttoned closing. As the 17th century headed to its close the sleeve turnbacks became real cuffs and got bigger. Into the early 18th century they got very large indeed, folding back to a depth as long as the forearm (buttoned, more buttons, to the sleeve to keep them in place), still displaying some extremely expensive lace ruffles and some of the fine linen of the shirt. By the time Beau Brummel had his sobering influence on English men's, and later most men's, fashions the coat had got generally plainer and often darker but the buttoned wrist opening remained, even if it was usually closed (Beau Brummel! Men certainly got cleaner and more streamlined, but rather less peacockily gorgeous). It could be opened to clear the hands of coat and shirt if necessary, but I can't imagine it often was - hand washing did occur sometimes, but that's another story...
So, this ability to turn back the coat sleeve was in existence for a very long time before a lone doctor had the lightbulb moment about washing hands and patients.