To tauten is to make something stretched tight, or for it to become stretched tight by itself. It works both ways: you can tauten a rope (you do it), or a rope can tauten (it happens). Think of a washing line with slack in it — pull the end and it tautens. The word belongs to rope, wire, cloth, sails, cables, skin: things with two ends that can be pulled straight. It is not a common word in daily conversation; people usually say 'tighten' or 'pull tight'. You meet tauten in writing — sailing, engineering, and especially in descriptions of a body: 'his jaw tautened', 'the muscles in her shoulders tautened'. Used that way it quietly signals that someone is tense or angry, without the writer saying so. Skincare adverts also love it ('tautens the skin').