The PlayStation 4 allows users to browse the web via an integrated web browser. As with most web browsers, your browsing history is saved. However, clearing your browsing history is very easy.
Clear Your Browsing History on the PlayStation 4
Open the web browser app and click the Options button on the controller to bring up the side menu. Then, go to Browsing History and press the Options button again. Select Clear Browsing History and confirm by clicking OK.