Just to add to Bill's addition...
Here is what Firefox says if you choose to browse "privately"...
Private Browsing
Firefox won't remember any history for this window.
In a Private Browsing window, Firefox won't keep any browser history, search history, download history, web form history, cookies, or temporary internet files. However, files you download and bookmarks you make will be kept.
While this computer won't have a record of your browsing history, your internet service provider or employer can still track the pages you visit.