Short answer
Private mode normally does not keep history, cookies and form data after the session, but websites can still see your IP address.
What is cleared
When the private window is closed, session cookies, page history and temporary data are normally removed from the browser.
What is still visible
Websites still see IP address, user agent and other technical information. Employers, schools or providers may also see network traffic depending on the environment.
When private mode is useful
It is useful on shared computers, for separate logins and temporary sessions, but it does not replace VPN or privacy protections.
Common questions
Does private mode hide my IP?
No. Your public IP address is still visible to websites.
Is private mode the same as VPN?
No. VPN changes the network path and the IP address websites see.