This is the 12326th most frequent Turkish word.
hatasını
"His/her/its mistake."
The word 'hatasını' refers to 'his mistake' and is composed of 'hata' (mistake) that is singular and 'sı' represents third person singular possessive, with the accusative suffix 'nı' indicating the direct object in the sentence.
Ahmet hatasını kabul etti.
Ahmet acknowledged his mistake.
Here, 'hatasını' again denotes 'her mistake' referring to Ayşe, and is used as the object of the verb 'fark etmek' (to realize).
Ayşe hatasını fark etti ama geç olmuştu.
Ayşe realized her mistake, but it was too late.
The word 'hatasını' in this context indicates possession ('his/her mistake') and is used as the object for the action described by the verb.