Every computer, or computer network, connected to the Internet has an address in much the same way every telephone has a telephone number. When you enter a URL (Universal Resource Locator), like this:
http://mainstreetmallonline.com/
into your browser's address window, your browser contacts an Internet system known and the Domain Name Service (DNS) which is somewhat like directory assistance for telephones. The browser looks up the URL to find it's actual Internet Protocol (IP) address with which it contacts the computer where the website is located.
If you don't have your own domain but host your site on someone else's, like this:
http://somedomain.com/myaccount/
it is like rooming with someone and using their phone. When you move, you can't take it with you. Not the phone or the web address!
No matter where you host your website, having your own domain means you have your own identity on the Internet and even if you move your website to another host (server) you will still be able to be found. A domain name can be pointed to any valid web address on the Internet, or it can refer to it's very own address -- YOUR Internet address!