Can anyone tell me what the meaning is behind the facebook "like" symbol and the number (x people like this) comment under my infomation on the main page?

It's the number of people who've clicked the little Like button next to that Facebook symbol. It somehow connects to PBS' Facebook page.

I'm still not understanding.  Is my avitar on face book and people vote on it?  When I click on the like button it prompts me to log into face book.  I don't have a account on facebook ( in the minority here) so I am not understanding the connection.  How are people voting and what exactly are they voting on?

Nobody is voting on anything. If you have a facebook account, and you click the button, you'll share the link with your facebook friends. It's just a way to share your interests with your buddies.

I can see how this would be confusing if you don't use Facebook. On Facebook, it's common for people to post things that say they like something. I might mark on Facebook that I like Dickens, or that I like a certain TV show, or that I like singing in the shower. When I say that on Facebook, all my friends get a message that says, "Beth likes singing in the shower."

PBS has made it easy for me to say "Beth likes Paperback Swap," along with a link to this site. All I have to do is click that button, and assuming I'm logged in to my Facebook account, all my friends will see something that says I like Paperback Swap. (I haven't done this exact thing so I might be getting some of the details wrong, but this is the idea.) Also, later, if people are checking out my stuff on Facebook, there is (I believe) a spot where the things I like is posted, and Paperback Swap would show up there. Good advertising for PBS.

If any of my friends had already "liked" PBS, then when I saw that PBS main page, it would say, "Jane Smith and Mark Austin like this." That could be useful information for me, if I was coming to PBS for the first time and trying to figure out if I was interested in it. I could contact them and ask them for details, for example, or I judge just based on that endorsement. 

I don't think that right under our personal information is quite the right place for it, because it's not clear what the "this" is that people are liking: it is Paperback Swap, not your personal information.

Hope this clarifies things!

Thanks everyone!  I get it now.  And yes, Elizabeth, where they have it is confusing.  I thought my profile was on face book when I am not even a member.