This is the 10783rd most frequent Turkish word.
demesi
The Turkish word "demesi" means "saying" or "the act of saying."
In this sentence, 'demesi' is used in its verbal noun form to indicate the act of saying or speaking about a specific subject by someone, in this case, the teacher.
Öğretmenin temizlik konusundan bahsetmesi herkesi düşündürdü.
The teacher's speaking about cleanliness made everyone reflect.
Here, 'demesi' is used possessively to associate the action of speaking with Ertuğrul, emphasizing his unusual statement.
Ertuğrul'un böyle şeyler demesi pek alışılmadık bir durumdur.
It is quite unusual for Ertuğrul to say such things.
In this context, 'demesi' refers generically to the act of saying certain words, and is evaluated for its fairness.