This is the 8112th most frequent Russian word.
латвийской
The word "латвийской" means "Latvian" (adjective, feminine, singular, or feminine genitive/dative case) in English.
In this sentence, 'латвийской' is used as an adjective to describe a 'писательница' (female writer), indicating her nationality.
Эта книга написана латвийской писательницей.
This book was written by a Latvian author.
Here, 'латвийской' modifies 'школе' (school), expressing that the school is located in Latvia or follows a Latvian curriculum.
Мы учились в латвийской школе несколько лет назад.
We studied in a Latvian school several years ago.
In this example, 'латвийской' characterizes 'культурой' (culture), indicating that the culture in question is from Latvia.