This is the 5845th most frequent Russian word.
районный
"Районный" means "district" or "regional" in English.
Here, "районный" is used as an adjective modifying "центр," denoting that the center pertains to a district or region.
Мой дом находится в районном центре.
My house is located in the district center.
"Районный" here qualifies "больнице," indicating that the hospital serves or belongs to the district.
В районной больнице недавно сделали ремонт.
The district hospital was recently renovated.
In this case, "районное" describes "управление," specifying that the administration operates at the district level.