For a domain name to be used it must first be registered and paid for by the person or company wishing to use it. This ensures that each domain is unique and avoids any conflict or confusion. Hosting is where a company or service keeps the files of your website on their server, so they can be accessed by other people on the internet. The up-side of these free services is that they often include a built in editor for beginners to create their new pages. The HTML produced by these is sometimes far from perfect, but they provide an easy way to get your site online while you learn.
Some services also supply in-house graphics and script libraries for their customers to use.
Something to be aware of, though is that some of these providers do not cater for what they call 'adult content' - and this includes any erotic or slash fanfiction. If you have this sort of material, you may want to check their policies before you sign up. Rates and services do vary, so make sure to shop around. Another page of Panthera's Lair Background by Panthera using pictures from The Force.