Some of the things myths explain are the traditions, morals, and customs of an ancient culture. They also explain the creation of the universe, world, people, and animals. Supernatural beings figure heavily in myths.
Legends are traditional folklore passed down generationally in oral storytelling that is historically based but embellished with details of mankind being helped by the supernatural at times. An example would be the Gods of Mount Olympus helping the warriors during the Trojan war. The city of Troy has been found. But definite proff of the Greek Gods has not been found.
A *fable* is a short moral story. The characters are anthropomorphized animals.
myth (m?th)
n.
1.a. A traditional, typically ancient story dealing with supernatural beings, ancestors, or heroes that serves as a fundamental type in the worldview of a people, as by explaining aspects of the natural world or delineating the psychology, customs, or ideals of society: the myth of Eros and Psyche; a creation myth.
leg·end (l?j??nd)
n.
1.a. An unverified story handed down from earlier times, especially one popularly believed to be historical.
1. a popular story handed down from earlier times whose truth has not been ascertained
2. a group of such stories: the Arthurian legend.
fable
fa·ble (f??b?l)
n.
1. A usually short narrative making an edifying or cautionary point and often employing as characters animals that speak and act like humans.
n
1. (Literary & Literary Critical Terms) a short moral story, esp one with animals as characters
http://www.thefreedictionary.com/Myth
http://www.thefreedictionary.com/Legend
http://www.thefreedictionary.com/fable