This is the 744th most frequent Russian word.
российская
"Российская" means "Russian" (related to Russia as a country).
In this sentence, 'российская' serves as an adjective modifying 'Федерация,' denoting the country's affiliation with Russia.
Российская Федерация является крупнейшей страной в мире.
The Russian Federation is the largest country in the world.
Here, 'российской' describes and specifies the type of school, emphasizing its association with Russia.
Она учится в российской школе, которая славится высоким уровнем преподавания.
She studies in a Russian school known for its high level of teaching.
In this example, 'российских' indicates the artists' origin or nationality related to Russia.