From Middle English herne, hyrne, from Old English hyrne ("corner"), from Proto-Germanic *hurnijō, *hurnijǭ, from Proto-Indo-European *ḱerh₂- ("horn"). More at hirn.
From Middle English hiren, hirne, from the same source as her. The -n was added (especially in the speech of the Midlands and Southern England, starting in the 1300s) by analogy with mine and thine. (Compare ourn.) Displaced in standard speech by the -s form, hers, which see for more. Cognate with West Flemish heurn ("hern").