Wiki Wrt 9 -Fable
Fables fall under the broader classification of Folktales. All folktales were stories that were told verbally to the listener. There were few books a long time ago, and so people memorized stories and told them over and over again to their family and friends. One type of story that they told was the fable.
Fables are short stories about animals, often personified, who either learn a lesson, or who teach a lesson. Fables have endings that state a moral. In other words, fables are short stories that have talking animals that learn a lesson.
Common lesson or themes that are taught in fables:
http://www.taleswithmorals.com/ (good site)