Takayama Jinya was the administrative center of the Edo shogunate’s direct territory. Simply put, and without fear of misunderstanding, you can think of it as something like a prefectural office, ward office, or city hall, or even a branch office of the national government, such as the Legal Affairs Bureau or Tax Office.
You probably have a city hall in the town where you live. It’s where you go to get your resident registration, apply for subsidies, and file complaints. The big difference between a city hall and Takayama Jinya is that it also houses the police force.