What is a Website Domain Name?
A website domain name is simply the named address of your website. Commonly, It's considered the stuff right after http://www or https://www.
As an example, the domain name for my website, which you are currently viewing, is matthewdevore.com. I actually have two domain names for this website. I just gave you the first. The second is matthewsdevore.com. Both domain names will send you to the homepage of this site. The second domain name is setup as a redirect. In other words, if you type www.matthewsdevore.com into your internet browser you will be sent (aka redirected) to www.matthewdevore.com.
Why use a redirect? There are a lot of reasons. An important one is to help people find your site. For example, I publish novels as Matthew S. DeVore, but my main domain doesn't include my middle initial. To help people find my site, I bought the second domain which includes my middle initial. Now people can use either and still find me.
Usually, website hosts and providers offer a free domain name for a specified period of time when you buy a hosting package. But after the introductory period, you'll be paying for the domain name separately. If you want a second domain name, then you'll buy that separately as well.
If you want to read more in depth about domain names, check out this article from HostGator: What Is A Domain Name?