First off, for all intents and purposes, the internet really doesn't care about domain names at all. It is merely a convenience put into place for us whereby some servers are allocated to do a translation of a domain name into an actual IP address. So in effect, when you type in
http://www.FaunaClassifieds.com into your browser, this information is relayed to a DNS (Domain Name System) server which will resolve that domain name to an actual physical IP address. That is how the page request from your browser on your computer winds up getting to the correct server, have that webpage retrieved, and then displayed on your browser. And here is the key here. The server that you request that webpage FROM has to know where to send it. In other words, it has to know YOUR IP address so that the page requested will actually get to you. So with every request you make of your browser for a web page, you are not only providing the address of the page you want, but you are also providing the address of YOUR browser on YOUR computer to which the server should send that page you have requested.
So in effect, your IP address, whether static or dynamic, HAS to tell the internet where you are so you can use the internet at all. You are setting up a specific mailing address on the internet so that when you are browsing, those servers you access know where to send everything your browsing requests of them. To them, it really doesn't matter whether your IP address changes from time to time, but it CANNOT change randomly while you are logged in, otherwise there is a chance that a change could take place AFTER a request to a remote server, and BEFORE that request can be filled and that page sent to you. In such a case, you would NOT get that page requested, because more than likely that IP address would (in dynamic addresses) belong to someone else. Certainly they would be disconcerted to have web pages showing up on their browser that they had never requested.
Of course, this is all a gross oversimplification of the process, but I think it gives a general idea of what is going on.