This is the 11487th most frequent Turkish word.
etkinliklerine
"Etkinliklerine" means "to their activities/events" in English.
The word 'etkinliklerine' in this sentence refers to activities ('etkinlikler') in their dative case ('etkinliklerine') indicating 'to their activities'.
Çocuklar okulun düzenlediği kültürel etkinliklerine katıldılar.
The children participated in the cultural activities organized by the school.
Here, 'etkinliklerine' is used to indicate the activities ('etkinlikler') in relation to the possessors, in this case, an implied group ('their activities').
Etkinliklerine herkes davetlidir ve giriş ücretsizdir.
Everyone is invited to their activities and entrance is free.
In this instance, 'etkinliklerine' relates to the activities ('etkinlikler') belonging to an entity (the festival), again in the dative case.