(2-part post):
There are (at least) two 'Rapidshare' services:
Rapidshare.com is a file-hosting service. It's used, for example, by people who want to send files to a friend (or group of friends) which are too big to be sent by email. The user uploads the files to the site and then provides the recipients with links to access the files. The site is not searchable so, unless someone provides you with a link, you can't download anything from it.
Rapidshare.org does not host any files on its own servers. It simply provides the user with 'peer-to-peer' file-sharing software. It also provides members with so-called 'support' (which hardly anyone would ever need to use, but is how they justify charging you to join). The file-sharing software accesses the same networks as programs like Limewire do. So basically, you're getting something similar to Limewire (which is available in a free version) but paying for it.