With private surfing, you can surf any website with out your activities being stored in the browser history. That is, all browsing history, temporary files and cookies will be removed upon closing your browser.
You can test this. After closing your browser, just type ipconfig /displaydns in command prompt (in Windows 7, right click Command prompt and Select Run as Administrator) and hit enter.
To clear all those details from your local DNS cache, just type ipconfig /flushdns in the command prompt and hit Enter.
Hope this will help you surf the Internet more privately.