This is the 729th most frequent Ukrainian word.
державного
"Державного" means "state" or "national," relating to the state or government.
Here, 'державного' refers to something belonging to or operated by the state, specifically a university.
Цей університет має статус державного.
This university has a state status.
In this sentence, 'державного' modifies 'бюджету' (budget) to specify it as the budget pertaining to the state or government.
Питання державного бюджету обговорювалося на засіданні.
The question of the state budget was discussed at the meeting.
Here, 'державного' describes the 'значення' (significance) indicating importance or priority related to the state.