This is the 1459th most frequent Turkish word.
ailenin
"Of the family" or "your family's" (possessive form).
In this sentence, 'ailenin' functions as a possessive noun, showing ownership of the house by the family.
Ailenin evi çok güzel.
Your family's house is very beautiful.
Here, 'ailenin' again denotes possession, indicating the decisions belong to the family.
Ailenin kararlarını destekliyorum.
I support your family's decisions.
In this case, 'ailenin' is used possessively to identify that the person is a member within the family.