Play which consists to try to make a trick with a card of intermediate value. The finesse is a "free fineese" when the player who does it plays the last (and consequently, without risking to lose the trick).
One of the wine tasting terms I most recommend avoiding because it is vague and anthropomorphic. When not applied to wine the term suggests "subtlety in performance, skill" (Random House Dictionary). Wine is inanimate, it has no skills, and does not perform. Subtlety is further defined as "elusively thin or tenuous" (Random House Dictionary) and these terms are not a compliment for wine. I suspect the term is most used to express admiration for the balance of a very fine wine. When the amount of fruit, acidity and tannins are harmonious enough to keep any one from standing out.
One of the simplest non-trivial card plays in bridge. The simple finesse looks like this: Dummy AQ Declarer 32 Declarer leads the 3 of the suit and if the next player does not play the King, declarer plays the Queen from dummy. If the player on declarer's left has the King, the Queen will take a trick.
In contract bridge and similar games, a finesse is a technique which allows one to promote tricks based on a favorable position of one or more cards in the hands of the opponents. If one can lead up to a finessable position such as ace-queen, an additional trick can be won if the king is positioned in front of the combination of ace and queen.