of, belonging to, made by, or done by them: often used with a singular antecedent (as everybody, somebody, everyone) to avoid the masculine implications of the traditional use of he without distinction as to gender, although this usage is objected to by some: did everybody finish their lunch?
Origin of their
Middle English theyr from Old Norse theirra, genitive plural of the demonstrative pronoun replacing Middle English here, Old English hira: see they