It's easy to dismiss myths simply as lies. After all, did Apollo really pull the Sun around in a chariot? Did Coyote really create the Indian tribes by flinging a defeated monster in several directions? Did Onamuji really die twice and have to be rescued by his mother? Who on earth is Onamuji? As children of the Enlightenment we have little patience for such absurd stories, condescendingly studying them (if we pay attention at all) as artifacts of primitive socities, or simply transforming them into comic book adventures.
Which is probably exactly what most of the originators of the myths would have wanted, at least the comic book part. As the great Roman poet Ovid demonstrated in his masterful Metamorphoses, myths aren't about telling what actually happened or describing the physical realities of the world so much as they're concerned with renewal, transfiguration and change.
There is a sense in which myths are intended to explain some perplexing aspect of the known world, as when the Scandinavians attributed lightning and thunder to Thor charging around in his goat-drawn chariot. But there's another sense in which it didn't really matter if they believed the stories they told at religious gatherings or by the fire at night; the mythologies of the Greeks, Chinese, Sioux tribes, Congolese and Slavs were all intended to impart to their listeners particular ideas about the world, about justice, about life and death, and about themselves.
Postmodernists like to call this sort of thing metanarrative, a universal story that imparts meaning on the chaos of existence. Men like G.K. Chesterton and J.R.R. Tolkien preferred to call it a search for truth. It was in this sense that Chesterton called the Christian Gospel a Myth—not because it was in any sense not true; quite the opposite, because it is perfectly true. Old mythologies worked hard to discover truth, while the Christian myth (the only completely true myth, as C.S. Lewis would say) is truth.
This is not to undermine the Christian narrative as found in the Bible, nor is it to apotheosize the ancient myths. There's plenty the old mythologists got wrong, and nothing untrue in the Word of God. Not only that, whereas the old myths are complete fabrications, the narrative of Scripture presents real historical events that actually transpired.
What is also true, however, and what is often ignored, is that what the Bible does for real, the myth-writers were trying to do. They wanted understanding, and the often bizarre stories they conjured weren't weird for the sake of weirdness: they were attempts at building a framework that would make sense of everything they knew existed, its origins, and its ultimate destiny.
Folklore shares a similar goal, though it's generally less universal, more homespun and culture-specific. Zeus is a mythic figure; Paul Bunyan is a folk hero. The folk hero is generally a national symbol, a human distillation of the peoples' spirit, someone they can identify with while looking up to them at the same time. Mythology and folklore often merge, especially in places with a long and deep heritage. The United States has no mythology, but its people have developed a rich folklore to make up for it.
At its best, mythology promotes noble conduct, self-sacrifice, and peacefulness. At its worst, it depicts a universe at the hands of capricious deities with appetites only different from ours in that they're bigger, more depraved, more destructive. We don't suggest building a worldview out of ancient myths, but if you have any desire to understand how people of the past thought and what motivated them, we do suggest starting with their stories.