go to history (above ont the left) and then to show 'all history'; right click with your mouse and take 'delete'. that's it

Selectively or all of it? Firefox has broadened their definition of history.

See

• https://support.mozilla.com/questions/902121
• Clear Recent History | How to | Firefox Help
  https://support.mozilla.com/kb/Clear%20Recent%20History
• Viewing the browsing history - Firefox - MozillaZine Knowledge Base
  http://kb.mozillazine.org/Viewing_the_browsing_history_-_Firefox
• the page is marked up for preserving history except for the cache
  http://img232.imageshack.us/img232/4928/clearcachew.png

This is a mobile question. None of the above links will work. In Firefox's settings you can use "Clear Private Data" if you want to remove everything but bookmarks. If you want control over what is being removed you can use the following extension https://addons.mozilla.org/en-US/mobile/addon/cleary/