This is the 14282nd most frequent Turkish word.
odasının
"Of his/her/its room."
In this sentence, 'odasının' is used as a possessive form meaning 'Ali's room', combined with the suffix -nin to show possession and relation to an action ('cleaning').
Ali odasının temizliğini yaptı.
Ali cleaned his room.
Here, 'odasının' signifies possession ('his room') and connects to the phrase to specify the location ('desk in his room').
Kitabını odasının masasına koydu.
He placed his book on the desk in his room.
In this case, 'odalarının' is a possessive plural form indicating ownership of multiple rooms ('his rooms').