Explained in two simple pictures:
(Images courtesy of the Coding Horror blog
Really, OpenID is merely a way for a third party (Google, Twitter, Facebook, etc.) to tell the site you are visiting that you are in fact a specific user on that service.
Want to try logging into a site with OpenID credentials to see how it works? You can try that out on Anthrocon's site
. I've got OpenID working over on PA-Furry.org