This is the 12874th most frequent Russian word.
латвийским
"Latvian" (adjective, relating to Latvia).
In this sentence, "латвийским" is used as an adjective describing "прохождение" (origin) related to Latvia.
Он гордится своим латвийским происхождением.
He is proud of his Latvian heritage.
Here, "латвийским" is used to describe "фольклор" (folklore), indicating that it pertains to Latvia.
Она занимается латвийским фольклором.
She studies Latvian folklore.
In this case, "латвийским" is an adjective describing "писателем" (writer), indicating their nationality or cultural background (Latvian).