The word redux comes from the Latin term reducere, which means bring back. This word is always used postpositively, coming after the noun it modifies, as in Rabbit Redux. In English, the term signifies that the noun it modifies has been revived, brought back, restored, or otherwise revisited. It is often implied that a work which is being revived has also been somehow changed, made more relevant, or given increased importance. This is often the case when artistic works are titled using the term.
Usage of this term was somewhat rarely evidenced before John Updike's Rabbit Redux came out in 1970. Before this book was published, the term was used in the titles of John Dryden's Astraea Redux in 1662 and Anthony Trollope's Phineas Redux in 1873. John Dryden's work is a poem in English, but the title itself is in Latin. This could be seen as the first popularization of the term in English. The term became relatively uncommon until John Updike's book revived its popularity.
Use of this term has also become quite popular in film and music. Francis Coppola used the term to entitle his re-release of Apocalypse Now which included materials that had been removed from the originally released version, as well as additional editing. Some musicians and music producers will describe what are normally thought of as remixes using the term as well.
This word is often used quasi-humorously to mean that a process has been repeated without being improved. One example of this usage is "company policy redux." In this sense, the term implies a sense of déjà vu, and not generally in a pleasant way. This is not to imply that all uses of the term have a negative connotation, but that context and tone play a very important role in the meaning of the word.
While this word is properly an adjective, it has recently entered the English language as a noun, typically in the form of "a redux of X": "a redux of last night," for example. This evolution of the term can be dated back to at least the 1980s, relatively soon after the release of John Updike's book. Even though there is no definitive evidence that the release of Updike's book caused this resurgence and evolution of the term, the book's popularity makes this a reasonable conclusion.
The term is also less commonly used as a verb, or as a stand-alone noun. As the word evolves, it continues to take on new possible meanings and forms. In the near future, it may come to mean, "doing it again" in some situations, as that is how it is often used as a verb.