This is the 5254th most frequent Polish word.
rodzinnym
"Rodzinnym" means "family-related" or "native" (depending on context).
Here, 'rodzinnym' describes the city that is associated with one's family or origins, functioning as an adjective connected to 'mieście' (city).
Mieszkam w rodzinnym mieście od urodzenia.
I have lived in my hometown since birth.
In this case, 'rodzinnym' describes the dinner as being familial, thus characterizing the type of dinner.
Spotkaliśmy się na rodzinnym obiedzie w niedzielę.
We met at a family dinner on Sunday.
Here, 'rodzinnym' is used to qualify 'domem' (home) as being related to the family, demonstrating possession or association.