c. 1200, "incapable of producing its kind" (of female animals, plants), from Old French baraigne, baraing "sterile, barren" (12c.), perhaps originally brahain, of obscure derivation, perhaps from a Germanic language. Use in reference to males is rare. Of land, "producing little or no vegetation," late 14c.
As a noun, mid-13c., "a barren woman;" later "tract of more or less unproductive land."
BARRENS. Elevated lands, or plains upon which grow small trees, but never timber. [Bartlett, "Dictionary of Americanisms," 1848]