La Llorona is told throughout the southwestern States and Mexico. Its origin is uncertain but it is quite old. There are a number of versions, which is true of all folk tales. It may have originated in Spain or it may be from colonial Mexico of the 16th century, where the story is known from Mexico City of the 1550s.
This website, at the State University of New Mexico, gives something of the story: La Llorona

A more complete history is available from the TCU website: La Llorona