A fig leaf is the covering up of an act or an object that is embarrassing or disagreeable. The term is a metaphorical reference to the Biblical Book of Genesis, in which Adam and Eve used fig leaves to cover "their nakedness" after eating the fruit from the Tree of Knowledge of Good and Evil.
In Ancient Greek art, male nakedness, including the genitals, was common, although the female vulval area was generally covered in art for public display. This tradition continued in Ancient Roman art until the conversion of the Roman Empire to Christianity, when heroic nudity vanished. During the Middle Ages, the nude was replaced by the naked and only the unfortunate (most often the damned) were usually shown naked, although the depictions were then often rather explicit. Adam and Eve were often shown wearing fig or other leaves, following the Biblical description. This was especially a feature of Northern Renaissance art.
From about 1530, the developing reaction to Renaissance freedoms and excesses that led to the Council of Trent also led to a number of artworks, especially in churches or public places, being altered to reduce the amount of nudity on display. Often, as in the famous case of Michelangelo's The Last Judgement, drapery or extra branches from any nearby bush was used. For free-standing statues this did not work well, and carved or cast fig leaves were sometimes added, such as with the plaster copy of Michelangelo's David displayed in Victorian era London. The Adam and Eve panels on the Ghent Altarpiece, already equipped with fig leaves by Jan van Eyck, were simply replaced with 19th century panels copying the figures but clothed. Many of these alterations have since been reversed, damaging some of the statues.
Eugen Sandow, often considered the first modern-day bodybuilder, was an admirer of the human physique, and in addition to strongman sideshows, he performed "muscle displays" by posing in the nude — save for a fig leaf that he would don in imitation of statues he had seen in Italy as a boy.
In the context of negotiation, an offer might be characterized as a "fig leaf" if that offer is actually a ploy to conceal a sinister plan.