Every web browser has some form of incognito or private manner. The browser will not record where you go, import your bookmarks, or mechanically log in to your accounts, when that private browsing mode is on. When you close the browser window, the browser will remove most of the info that someone could utilize to retrace your steps.

But a private mode will not keep your identity anonymous. Any files while browsing in a private mode which you download will stay on your smartphone or your personal computer after the browser closes.