It was a while since I set mine up, but I think it goes like this.
You buy and register a domain name, and usually this is done via a company that will host the domain. Then they can provide email accounts for that.
E.g.you buy
www.mydomain.com, then you can set up pretty much any email account with that address:
something@mydomain.com
You have to pay the hosting company a fee (not a lot), and they will usually pay the company that has the domain registered.
So as you own
www.mydomain.com provided you keep paying the registration
company, you can change the company that hosts it and provides your email if you wanted to.
often there are cheaper domains than .com e.g. in the uk co.uk
Someone correct me if I am wrong - but that is my understanding.