The state of NH runs on a a multi-billion dollar budget.
Revenue sources include federal revenue, various taxes and fees, lottery and liquor revenue among others.
Some of the services include law enforcement, business regulation, maintenance of highways and bridges, infrastructure projects, health care and education.
These two pages provide a good overview.
Note that the biggest revenue sources in the general revenue category are business taxes and the Rooms & Meals tax.
( The state property tax is actually larger than the R&M tax, but it is dedicated to local education expenses ).
One thing that link does not make clear is the revenue sharing from the state to towns. That can be found in your town/school report.