It seems that you want to use a domain such as example.com. Maybe it's your first site, so I explain a little bit.
You can use a domain without purchasing it, just on your computer for testing purposes, by configuring the /etc/hosts file.
On the other hand, to use the domain for your online website so that people can see it from any computer, you need to purchase a domain name at a registrar like Hover or similar.
And you need a copy of your site on a public VPS. For example, I like Linode, with daily backups and very good service. However, NodeBB people offer a few free months at another good one, DigitalOcean. Anyway, these web hosting services are not expensive (affordable unmanaged VPS).
At NodeBB they also offer managed hosting for large forums, doing the technical tasks for you, but of course it's a different option that comes with a cost.
The software itself is open source and can be used for free if you do the technical maintenance by yourself.