This is the 3868th most frequent Turkish word.
ailemizin
"Of our family"
In this sentence, 'ailemizin' is used as a possessive construct meaning 'of our family', showing possession of 'evi' (house).
Ailemizin evi sahilde, çok güzel bir yer.
Our family's house is on the beach, a very beautiful place.
Here, 'ailemizin' indicates possession, referring to the family as the provider of the 'desteklerine' (supports).
Ailemizin desteklerine güvenerek projeye başladık.
We started the project, counting on our family's support.
In this usage, 'ailemizin' modifies 'bireyleri' (members), showing they are members belonging to 'our family'.