A domain name is the web address people type into a browser to reach your website, such as yourbusiness.com. You do not buy it outright; you register it, usually a year at a time, through a registrar.
For a small business, the domain is the one asset you most want held in your own name. When a web person or agency registers it under their account for you, they hold the keys to your address, and moving your site later can turn into a hard conversation, or the loss of the name entirely. Ask whose name and email are on the registration, and make sure they are yours. The domain is separate from your web hosting, where the site’s files actually live, and separate again from the site itself, so who owns the website is a second question worth asking plainly.
I register every domain in your name, with your email as the account owner, and point it at the site so it loads over a secure HTTPS connection. If you already own your domain, it stays yours: I connect to it and hand back the keys. You should be able to walk away with your address at any time and have it still work.