What is a fable?

From Wikipedia:

A fable is a succinct fictional story, in prose or verse, that features animals, mythical creatures, plants, inanimate objects or forces of nature which are anthropomorphized (given human qualities), and that illustrates a moral lesson (a “moral”), which may at the end be expressed explicitly in a pithy maxim.

A fable differs from a parable in that the latter excludes animals, plants, inanimate objects, and forces of nature as actors that assume speech and other powers of humankind.

From Composition in the Classical Tradition:

The fable is a short, fictitious narrative designed to teach a moral lesson or make a cautionary point. The purpose of the fable is to give advice, to exhort the reader or listener to pursue a wise and prudent course of action, and to dissuade the reader or listener from foolish or imprudent behavior. The fable is not intended to stand alone as a literary object. It functions as an illustrative example in a deliberative speech or essay as a form of proof.
D’Angelo, Frank J. Composition in the Classical Tradition. Needham Heights, MA: Allyn & Bacon, 2000. Print. (59-60).

From Writing about Literature:

A Fable Is a Short Tale with a Pointed Moral

The fable (from Latin fabula, a story or narration) is an old, brief, and popular form. Often but not always, fables are about animals that possess human traits (such fables are called beast fables). Past collectors and editors of fables have attached “morals” or explanations to the brief stories, as is the case with Aesop, the most enduringly popular of fable writers. Tradition has it that Aesop was a slave who composed fables in ancient Greece. His fable “The Fox and the Grapes” signifies the trait of belittling things we cannot have. More recent popular contributions to the fable tradition include Walt Disney’s “Mickey Mouse,” Walt Kelly’s “Pogo,” and Berke Brethed’s “Bloom County.” The adjective fabulous refers to the collective body of fables of all sorts, even though the word is often used as little more than a vague term of approval.
Roberts, Edgar V. Writing about Literature. 12th Edition, New York: Prentice Hall, 2009. Print. (161).