The private browsing is useful when browsing websites on other people’s device because it leaves no footprint after you close the browsing tab. The feature actually isn’t new, and has been available in iOS 6 for quite a while.
To access, open Safari’s tab screen where you see the fancy 3-D tabs stacking on each other, and tap Private button at the bottom left corner.
What did change in iOS 7 is that you won’t be able to find the Private setting from Settings. Hence, the Private mode is now only tab-based.