This is the 8622nd most frequent Russian word.
оршанского
"Оршанского" is the form of an adjective meaning "of or related to Orsha," a city in Belarus.
In this sentence, 'оршанского' is used as a genitive adjective, indicating a possession or belonging to the place Orsha.
Я встретил старого друга оршанского училища.
I met an old friend from the Orsha school.
Here, 'оршанского' describes the museum, meaning it pertains to or is located in Orsha.
Экспозиция оршанского музея включает уникальные экспонаты.
The exhibition of the Orsha museum includes unique exhibits.
In this case, 'оршанского' modifies 'району' (district) to specify the district related to the location Orsha.