Clearly, you're interested in the nicety of a word's meaning if you're checking out this website. A nicety is a fine detail or shade of meaning that anything — not just a word — can possess.
Even the word nicety has niceties. The emphasis on detail can also refer to a precision or accuracy of sorts; if someone has judged something "to a nicety," they've judged it exactly. Yet another common meaning is in the sense of a minor aspect of polite behavior. Washing your hands before dinner is a "social nicety." So is covering your mouth when you cough. Now where would we be without niceties?