This is the 117th most frequent Russian word.
российского
"Российского" means "of Russia" or "Russian" (relating to the Russian Federation).
In this sentence, 'российского' functions as an adjective describing 'art' that pertains to Russia or Russian culture.
Я посетил музей российского искусства.
I visited the museum of Russian art.
Here, 'российского' modifies 'magazine', indicating that the magazine is published in Russia or is of Russian origin.
Вы любите читать статьи из российского журнала?
Do you like reading articles from a Russian magazine?
In this example, 'российского' describes 'university', specifying that the university is located in Russia or is Russian.