The buffalo allowed the woman and her father to go, on condition that they learn the dance and song of the buffalo, and not forget them. For these would be the magical means by which the buffalo killed by the people for their food should be restored to life, just as the man killed by the buffalo was restored. This myth tells the people why they do the dance, and the consequences if they don't. It is also a piece of sympathetic magic designed to increase the fertility of the buffalo herds when the dance is performed. As such it gives them a sense of control over some of the important factors of their environment and indicates appropriate action if the buffalo do decline.
Myths also have a descriptive function, explaining facts beyond normal reason and observation.
Creation myths are an example. The Norse creation myth describes Niffleheim forming out of the Abyss, with ice to the north and fire to the south. From the melting ice where these two realms met formed a giant, Ymir, and a cow, Audmulla, who became the wet-nurse of the gods. From Ymir came the frost giants, and Audmulla's licking of the ice freed the progenitors of the gods, Odin, Vile and Ve. And so the myth goes on, describing the creation of the world, the gods and mankind.