According to Wikipedia, the phrase dates from at least 1968 and was popularised by Jan Harold Brunvand, professor of English at the University of Utah, in a series of popular books published beginning in 1981.
Now I thought that that there was something specifically urban about urban lengend, but checking around it actually looks as though an urban legend is really quite close to what Australians would simply call a yarn. I quote one definition:
Question: What is an urban legend?
Most people have heard the story, usually imparted as a thing that "really happened to a friend of a friend," of the dotty grandma who tried to dry her damp poodle in the microwave. The dog exploded, sad to say, and Grandma has never been quite the same since. The story isn't true, of course; it's an urban legend circulating since the 1970s. It describes a mishap that could have happened, but we have no evidence, nor any good reason to believe, that it ever really did. And there's a moral: newfangled technologies, albeit a boon to humanity, can also be dangerous when misused. It's a horror story with a point!
Answer: An urban legend is an apocryphal, secondhand story, told as true and just plausible enough to be believed, about some horrific, embarrassing, ironic or exasperating series of events that supposedly happened to a real person. As in the example above, it's likely to be framed as a cautionary tale.Actually, all this is mildly disappointing. The real significance of urban legends lies in the use of the word urban. The tales themselves aren't new, only the specific use of the word urban to describe them, a sign of the growth of the cities.
Whether factual or not, an urban legend is meant to be believed. In lieu of evidence, however, the teller of an urban legend is apt to rely on skillful storytelling and reference to putatively trustworthy sources — e.g., "it really happened to my hairdresser's brother's best friend" — to convince hearers of its veracity.