A Domain name is YOUR business name on the world wide net,
for example www.bbc.co.uk or www.microsoft.com
The domain name is a very important part of anyone's web-site as visitors use it to find you on the www.
It is important to keep hold of the domain name, web-sites can easily be reproduced, a domain name, if you let it lapse and someone else registers it, it's gone and is very difficult and costly to get back.
The actual physical location of the web-site is not important, wherever it is hosted, in whichever country, visitors can find it by using the domain name.
How it works.
You want to view a web-site, you type in the address, www.sally-dog.com, your computer sends the request for the first page of the site to your ISP. Your ISP looks up the physical address in it's database [dns] and routes the request on via other networks to the actual server the site is located on. The web page and all it's eliments are then sent over the internet to your computer ready for your web browser to display.
A domain name and actual web-site can be hosted on different servers and in different country's. The domain name points to the physical web-site.
The domain name holds the address of where the web-site resides. If you move the web-site to a different server all you have to do is update the domain name to point to the new location, this in turn updates the dns servers which are used to look up the web-site, meaning your web-site will still be reachable by visitors.
Remember your domain name is very important, a web-site can easily be replaced, the domain name can't, look after it.