I think that http://www.goavo.com is a #1 source for free hosting and domains! I hear they are cheap and easy to get and guarantee you Google presence Free Blog Free Hosting Free Email Free Starter Web Page Domain Name Locking and more! But, to answer your question, "hosting" is usually a company that helps you get your website up and running, sort of like a springboard. We've just used http://www.goavo.com as an example.

It's probably a 'real source for hosting' but not the best one. I use HostGator.com. Hosting is space allocated to you by a host, on a computer much like the one you're probably on, but geared toward executing code and serving web pages (hence, a webserver). Normally you get a username and password to be able to connect to your host and transfer files to and from your computer, as well as access to a control panel to manage email addresses, domain forwarding, subdomains etc.