So called private browsing has become a big addition to the current generation of browsers, and they all do it slightly differently.
Close 'n Forget is an add-on for Firefox that gives you another way to remove evidence of where you've been browsing. In the options menu, you can choose to have Close 'n Forget remove the history for the whole domain you're on, or just that page, or just those viewed in the tab you're closing, and finally you can opt to remove cookies from one or all of the pages in a domain.
Being able to quickly remove cookies from a page using the right-click context menu is nice, and really useful even if you're not interested in deleting your history. You delete a tab now using a right click, when you can select close and erase, and depending on your set up, some of that page's history will be deleted. It's a system you can easily get used to, and some users will no doubt find it less laborious than going in and out of Private Browsing mode.