With ‘Clear Recent History’ dialog in Firefox (which you can open on Windows by using Ctrl+Shift+Del or by visiting  Options > Privacy > clear your recent history), you can clear browsing data and other stuff, where newly added ‘Forget’ button to the Nightly on the toolbar lets Firefox to forget about some browsing history for the last five minutes, Two hours or twenty four hours.

Firefox Forget button

This is more of a stripped down version of the Clear Recent History feature, this button when you click on after selecting a time frame, deletes recent cookies, history and closes all tabs and Windows and opens a new clean window.

And Forget button in new window shows a dialog with text ‘your recent history is cleared. Safe browsing! Thanks!’.  

Firefox with Forget button on navigational toolbar

Note: In Nightly, by default, Forget button will be hidden in Customize window, you need to drag and drop it onto either toolbar or menu.