The folks at WebmasterWorld really look at every fine detail when it comes to Google's search behavior. Moderator, Receptional Andy said he noticed that when searching in Firefox at Google, Google would append an HS parameter in the URL, when clicking from search result page to search result page.
For example, conduct a search for anything at Google using the Firefox search bar. Then move your mouse over the next link at the bottom of the Google results. If you look, you will notice an HS parameter. It looks like this:
It is not found in the first search URL, but only when you click next and only when the search is initiated when using the Firefox search bar. Here are the parameters I find after the HS=, cWW, hyB, oyB, WJr, and they keep going.
What does it exactly mean? I am not sure. It seems to be assigned on a page by page level, and only with Firefox.
Forum discussion at WebmasterWorld.