A fan page, also known as a Facebook Page, is like a FB page for your business. You can post to the wall, use RSS to publish your blog, start discussions, post images and get feedback from your fans. The main difference is that there are no "friends". Instead of friends you get fans.
When you click "become a fan" then you will get updates when that person updates the page. For example when I post new images or that I'm looking for new models on my fan page then it shows up on the fans home page. However because they are not necessarily friends I do not get their postings on my personal FB home page.
For more info here is a link to Facebooks info page about them. http://www.facebook.com/advertising/?pages
You can search for it on Facebook just like you would search for a friend. After you get 1,000 fans the site will let you have a custom name so that the link it easier to find.
A search for any well known actor or musician should bring up plenty of fan pages. If you want to check out mine it's under Azure LaRoux http://www.facebook.com/pages/Azure-LaRoux/159159624134799