How to stop or edit private browsing

On iOS, Private Browsing runs in a separate window (or windows) from non-private browsing windows.

To switch between them, tap the overlapping page icon in the top right corner:

Then you can switch between Private and normal browsing modes using the tabs at the top of the screen:

Switching between private and non-private just hides the other mode's pages. You can click the x icon in each respective tab to close the page.