In a dream, a fable usually signifies some moral lesson about the reality. In other words, the dream is telling someone what they should be doing or what they are doing in their life.
However, it is usually not quite that simple. Sometimes the moral of the story may also have an additional meaning other than a simple lesson and sometimes there may be more than one meaning in one story.
A common meaning for fables in dreams is to face reality and live life with more honesty and integrity. This can mean getting over your fears, which might be preventing you from moving on with your life and making progress towards your goals. Another way to interpret this could be as a call to action, either by facing fear or taking corrective action. Both of which could lead you to a better outcome than staying still.