This is the 2725th most frequent Turkish word.
çiftinin
"Çiftinin" means "of his/her/its pair" or "of the pair" in English.
Here, 'çiftinin' is used in the possessive form to indicate ownership or relation, specifying the nest belonging to the pair of pigeons in the garden.
Bahçedeki güvercin çiftinin yuvasını temizliyoruz.
We are cleaning the nest of the pigeon pair in the garden.
In this sentence, 'çiftinin' indicates possession or description of pairs, belonging to the set of jewelry items.
Takının altın çiftinin her biri 22 ayar.
Each of the gold pairs in the jewelry is 22 carats.
In this context, 'çiftinin' refers to the possessive form describing the story that belongs to or is about the couple in the movie.