The tale of the Turtle and the Rabbit. The turtle agrees to race the rabbit and in the mean time the rabbit decides he is too fast and takes a nap, and here comes the turtle, slow as a turtle, and came and beat him.
The meaning that Midori attributes to this piece of folklore is that patience is always going to get you what you want. She thought that the turtle won because he was simply more patient when it came to getting somewhere. She believes that this is the same in life for everyone and that we should all be slow and take the time that we need to accomplish a task.
I think that she heard this tale originally as a Tortoise and the Hare, but I am not sure. She could not remember exactly when or where she heard it. She did remember though that it was during her childhood that she heard the tale. If the case is that she has changed the characters I believe this is just a very good example of variation then. I know of the cartoon versions of the Tortoise and the Hare, but I have had her tell me the Turtle and the Rabbit before.
This just shows how different pieces of folklore can still have the same meaning. It also shows how sparse the tale really could be and still be able to get the message across to the listener.
I believe that the meaning of this tale is that of being humble. I think that because the Rabbit, or Hare was so cocky that he made a mistake and that had he been more humble that he would have won easily. Taking either meaning for the tale, it is most likely going to be popular among younger people, or older people. Older people relate to the story for they have generally become more patient over time, whereas younger people can be told this tale and gain a lesson from it, either to be more patient, or to be more humble.