Fables are stories which contain a moral or convey a lesson. Reknow fables include the Fox and the Grapes, in which the fox convinces himself that the fruit he cannot reach is not tasty and the Tortise and the Hare which shows slow and steady wins the race.
There is the story of the turtle and the hair,and the frog that wanted to be as fat as a cow. Fables are stories that have a moral in them. Basically you should not try to be what you are not, it's best to stay yourself.