their is a possessive pronoun: as a possessive marker it modifies the noun 'time' and as a pronoun it refers back to 'They'.
They took they're time.
they're is a subject pronoun (i.e. they) plus a contracted verb (i.e. are). Simple sentences have only one verb phrase, not two as in 'They took' and 'they're'. Subject pronouns (e.g. They, We, She) occur before the verb and object pronouns (i.e. them, us, her) occur after the verb. The pronoun 'they' cannot modify a noun. 'their' is used to modify a noun.
They took there time.
there can be an adverb of place (e.g. I agree with you there) or a noun of location (e.g. They took us there - to that place).
their(is apossesion prounon of there) for instance
he-his (he has agood cell phone- did u see his mobile phone?)
she-her (she has new notebook - did u see her new notebook?)
they-their (they have their luggages- they prepared they luggages for travelling.)
here, there . we are using them when we refer to specific place, this place almost near.
here ( can u come here plz?)
there ( can u see them there?, yes i can)