La llorona is a folktale told throughout Mexico and the American Southwest. It tells about a young woman, her wealthy husband, and her children. For an extensive look at this legend, try this article from a New Mexico newspaper, 2007, by Paul Harden.
http://www.caminorealheritage.org/PH/1207_llorona.pdf
Also check the Canciones / Songs / Música section of this blog for three versions of the song, Llorona.