A fable is a fictitious story made up or told to illustrate or teach a moral. Though many popular and famous fables do feature animals, that behave in some respects like humans, - for example, they may talk like humans - this is not an essential characteristic of a fable. For example, all characters in the famous fable titled Kings New Clothes, by Hans Christian Anderson, are humans. Fables may also feature forces of nature as characters in the story. For example, in a popular fable, that highlights the superiority of power of love and understanding over that of physical force, there a contest between the Sun and Wind which involves taking off the coat of a traveller. The wind tries to blow the coat off the traveller but fails to do so. But when the sun makes the weather warm, the traveller takes of the coat on his own.
Generally, we associate fables with the stories that have been told for many centuries. Morals of many such fables, summed up in short phrases, have become well known proverbs. For example, when we speak of 'sour grapes', we are referring to the moral of the famous fable titled The Fox and the Grapes.
The fable as a genre features animals with human traits who carry on a brief action illustrating truths about human beings. The use of animals as protagonists (and antagonists also) enables the fabulist to concentrate on the topic without complications. It is perhaps one of the oldest and simplest of all the stories to tell, and did not require vast amounts of memory in order to retell the tales. They formed the very basic and essential elements to live a fulfilling life without pretension, stress, and anxiety about others, and in promoting one's positive values as an influence upon others. The stories are literary as well as didactic.
A fable is any peice of literature that involves the teaching of a moral. Aesop's fables are example. Also Peter and the Wolf is a fable.