Most people have no idea of how closely everything they do is tracked on the internet. A web browser, like Firefox, is called a User Agent. In other words, the browser acts on the user's behalf. Web browsers, by default, are not acting in the user's best interest and are generally bending over backwards to share more information with websites visited than is necessary.

First of all, when performing a search on a search engine, the search query is generally stored in the URL of the search results. When you click on a link from one site to another, your browser sends a bit of information in the request that identifies the URL that the request was linked from. This is called the REFERER header (yes, it is misspelled). Since your search results page contains the search you performed, your web browser is volunteering this information, so the web site you visit knows the search text you performed to find their page. It's not required to send that information, but your web browser, acting as your agent, gladly gives that information. You can change this default behavior with a Firefox plugin called RefControl. After installing it, you must change the default settings to actually block that information. I set the default to block 3rd party REFERER information which blocks links between different web pages, like the search engine link example.

Web pages contains bits of code and assets housed on separate servers which exist just to track your movements on the web for purposes of targetting advertisements etc. Usually this slows down page load times and allows ad networks (and Facebook, Twitter, Google, etc) to track your movements around the web. There's a plugin to block that, too, called Ghostery.

I think the default browser behavior is terrible regarding privacy, and these addons give users control over how much information they want to share.