What hiding your IP does
Sites and apps stop seeing your provider and your city. Your provider stops seeing which sites you open (with a VPN or Tor). On café and hotel Wi-Fi, people on the same network can't see where you go. Is the Wi-Fi you're on safe?
What it doesn't do
If you log in to an account, the site knows it's you anyway. Cookies and your browser's details (language, screen, fonts) still identify you to some degree.
Check that it worked
Turn your VPN on and open the VPN test: it checks the address, WebRTC leaks and your clock.