This is the 12412th most frequent Russian word.
католической
"Католической" means "Catholic" (adjective, feminine form) in English.
Here, "католической" is used as an adjective describing the type of school.
Она учится в католической школе.
She studies in a Catholic school.
In this sentence, "католической" modifies "церкви" to indicate the religious affiliation of the church.
Католической церкви уже много веков.
The Catholic Church has existed for many centuries.
The word "католической" specifies the particular faith being referred to, highlighting its Catholic nature.