This is the 303rd most frequent Romanian word.
familiei
"Familiei" means "of the family" in English.
Here, 'familiei' is the genitive form of 'familie' (family), meaning 'of the family'. It is used to indicate possession, referring to 'my family'.
Membrii familiei mele sunt foarte apropiați.
The members of my family are very close.
In this sentence, 'familiei' is again in the genitive case, specifying ownership, indicating that the house belongs to the family.
Casa familiei este decorată cu flori.
The family's house is decorated with flowers.
'Familiei' involves the genitive usage that implies association or belonging, indicating the meeting is of/for the family.