A myth is a story. The Greek word mythos means "story." That's the basic concept. But, of course, not just any old story can be a myth. If you happen to be served a whole pig's head for dinner in Thailand — it's a good story and one worth telling, but it isn't a myth. You may know a myth when you see it, but you still need some kind of definition before you can get down to the business of fully appreciating myths.
Experts love to argue about difficult, hard-to-define subjects, and mythology has been a popular topic for argument for the past two centuries. Scholars argue about what is a "true" myth as opposed to some other kind. They insist, however, that no one confuse myths with other similar types of stories, such as legends, sagas, and folk tales.
Specifics of mythological proportions
So what's special about a myth? Well, myths are stories about gods and goddesses and supernatural entities and human relationships with them. This definition can expand to include stories that explain universal truths or values and stories that help groups of people (such as Americans) identify themselves and define their values. Myths help validate the social order, such as hereditary kingships or social class structures. They also can provide a "history" of a kingdom that makes it seem inevitable.
Because myths are about humans and the gods, then they're also always about religion. Most myths were or are still part of a religion that people practiced seriously.
The word myth has come to mean "untrue" in some contexts; people say something is "just a myth" if no factual basis exists for it. But myths do have their own truths. They provide people with a view of the world and a set of values that can be as important as any scientifically verifiable fact.
Legends
Legends are similar to the myth, but they're based on history. It doesn't have to have much of a historical basis — many legends hardly jibe with the historical versions at all. A legend or saga, however, does have to include something that actually may have happened. For example, the story of King Arthur is a legend because there (probably) was an actual man who served as the basis for the King Arthur you know of today.
Folk tales and fairy tales
A folk tale is a traditional tale that is primarily a form of entertainment or, in some cases, is used to instruct. Folk tales involve adventures, heroes, and magical happenings, but they don't usually try to explain human relationships with the divine.
Most stories known as myths have elements of legend or folk tale in them and vice versa. These terms are useful in helping determining what is and isn't a myth, but you shouldn't get too hung up on them.
Fairy tales look like myths and folk tales, but they're a little different. Fairy tales came out of the Romantic Movement of the 19th century, when people such as the Brothers Grimm collected stories from local people and wrote them up in romanticized versions. The Grimm fairy tales, however, are nothing like the sanitized, modern ones — the original versions are full of blood and brutality.