In Greek mythology, Libya, like Ethiopia or Scythia was one of the mythic outlands that encircled the familiar Greek world of the Hellenes and their "foreign" neighbors.
Personified as an individual, Libya was the daughter of Epaphus, a son of Zeus and King of Egypt, and Memphis. Libya was ravished by the god Poseidon to whom she bore twin sons, Belus and Agenor. Such genealogies, when applied to a personification of a land, were suggestive to Greek audiences, but need some explication for ordinary modern readers.
(some cautious explanation of the cultural/legendary meaning of this genealogy is needed)