Their is the possessive form of the pronoun they. Theirs is a possessive pronoun, the absolute form of their. Their is used to qualify a noun that follows: "their dog," "their car." Theirs is used in other constructions: "a dog of theirs," "all theirs." Their means "belonging to them" and should be kept distinct from there and they're. Their is never written with an apostrophe (theirs, not their's). See also they.
Dictionary of problem words and expressions. Harry Shaw. 1975.