Private browsing is the act of using a web browser without it storing the information from the sites you visit (e.g. browser history, cookies, temporary files). If you're asking about the Tor network, please use the tag for Tor.
Private browsing may be known by different names for different browsers:
Firefox: Private Browsing
Chrome: Incognito Tab or Window
IE: InPrivate Browsing
Safari: Private Browsing
Opera: Private Tab or Window
Silk: Private Browsing
Dolphin: Private Mode
Private browsing allows the user to browse the internet while disabling browser history and temporary files (cache). This can be useful when a user would like to test a site where cache already exists in the browser. It can also be useful for searching for terms that you would otherwise not like remembered.
It is important to remember browsing privately turns off history and cache for your browser, but it does not make your unencrypted web traffic private to your network or ISP.
For questions about Tor and .onion sites, please use tor.