This is the 18262nd most frequent Russian word.
чью
"Чью" means "whose" (feminine, singular).
The word "чью" here is used as an interrogative pronoun in the accusative case, asking 'whose' with 'bag' being feminine singular.
Чью сумку ты взял из прихожей?
Whose bag did you take from the hallway?
In this example, "чью" serves as a relative pronoun, referring to 'whose' book, with 'book' also being feminine singular accusative.
Я не знаю, чью книгу я взял по ошибке.
I don't know whose book I took by mistake.
Here, "чью" indicates possession in a subordinate clause, relating to 'whose' clothing, in feminine singular accusative.