Read about it at TYWKIWDBI -- but first, the classic example of a mise en abyme in art is Arnolfini Betrothal by Jan Van Eyck (1434). Can you guess what the term means before you click on the link? (However, the Arnolfini painting is not an example of the Droste effect -- and JWebb gets Scribal points for explaining that the van Eyck is "not truly recursive because the mirror shows not only different people from a different view, but there is no mirror behind them to carry out further iterations.") The Droste effect is an illusion of infinite repetitions, but the mise-en-abyme (placed in infinity) technique can be interpreted more loosely as suggestive of a "world within a world."
The word "abyme" is spelled abîme in modern French and is the root of our adjective, abysmal. (When a French vowel is wearing a "little hat," it means that an /s/ has been removed from an earlier form.) English used to have the noun "abysm," based on the French, but it was later changed to sound more like the Latin root, abyssus, so the modern English noun form is now "abyss."