This question tests the use of plurals and possessives.
(A) Childran is not a word; the plural of child is children.
(B) Children is already a plural noun. It does not take an 's' at the end to make it plural. Childrens is incorrect.
(C) Children's books uses the apostrophe 's' ('s) to show possession. It means books belonging to children. This is the correct way to form the possessive of an irregular plural noun.
(D) Child books could be used in some contexts (treating child as an adjective), but the standard and correct way to express possession is with an apostrophe.
Therefore, Children's books is the correct expression.