"portion," Old English scearu "a cutting, shearing, tonsure; a part or division," related to sceran "to cut," from Proto-Germanic *skaro- (cf. Old High German scara "troop, share of forced labor," German Schar "troop, band," properly "a part of an army," Old Norse skör "rim"), from PIE root *(s)ker- (1) "to cut" (see shear).
Meaning "part of the capital of a joint stock company" is first attested c.1600. Share and share alike attested from 1560s. The same Old English noun in the sense "division" led to an obsolete noun share "fork ('division') of the body at the groin; pubic region" (late Old English and Middle English); hence share-bone "pubis" (early 15c.).