The hosting is a monthly fee, which is what "puts" the forum on the internet.

The domain name is a yearly fee and its the www.--.com of the website and that's the address you type in the access the forum files/scripts being hosted Online.

The hosting and domain can be bought through the same company, or different company, so you will want to ask the person your buying from who hosts the website, and the domain and how much are they montly and yearly?

Next is what Lisa said, what is the software(script) they are using that runs the forum. What is the yearly renewal cost if any..