iPage's web hosting packages start as low as $1.99 per month and they throw in domain registration for free during the first year, which makes them a bargain for very, very lean startups or one-person operations. They also have the classic domain name search portal, and provide a tutorial on the new TLDs that helps, considering a new one seems to be appearing every second or two.
If you ever change your web host (the actual physical location of your website files), your domain name goes with you. Your regular visitors or customers who knew your site name as (say) www.thesitewizard.com would not have to be informed about a change of web address (also known as "URL"), since as far as they are concerned, the site is still at the same place. They would simply type your domain name and they'd be transparently brought to your new location.
Your domain name is how visitors easily find you online. It is often the first step in getting your website started because it is like establishing your website’s street address on the internet. If you did not have a domain name, you would have to give out your IP address to everyone who wanted to visit your website, which would get confusing and be easily forgotten.