This is the 771st most frequent Russian word.
харьковской
"Харьковской" means "Kharkiv's" or "of Kharkiv," referring to something associated with the city of Kharkiv.
In this sentence, 'харьковской' is used as an adjective to describe the type of history being discussed, specifically related to the city of Kharkiv.
Я читал книгу о харьковской истории.
I read a book about Kharkiv history.
Here, 'харьковской' describes the school, indicating that it is located in Kharkiv or associated with that city.
У нас новый проект для харьковской школы.
We have a new project for the Kharkiv school.
In this example, 'харьковской' modifies 'научное достижение' to show a relation to Kharkiv, emphasizing the origin or association of the scientific achievement.