The word their is a possessive pronoun that is used as an adjective. Use the word their with a noun.
My parents bought their house in 1957.
The possessive pronoun their modifies the noun house.
The word theirs is a possessive pronoun that stands alone as a pronoun, taking the place of a noun.
My parents bought a house. The house is theirs.
Here are more examples:
Jan and Bob are proud of their children. The children are theirs.
My brothers painted their room blue. The room is theirs.
The words their and theirs are possessive pronouns. Use their to modify a noun. Use theirs as a stand-alone pronoun.
▶It’s your turn. Decide if you should use their or theirs in the blank. My neighbors are happy that I found ____ dog. Did you choose the word that modifies a noun? Good for you!