It’s pretty simple. A VPN adds a layer of privacy between you and the server you’re accessing. You go from user A with X home IP address originating from precise Y location, to user A with generic shared IP originating from a vague location likely nowhere near your real location.
Beyond location, did you know there are services that can sometimes accurately provide a users place of work based on home IP? Their likely income level, and more. That becomes impossible with a VPN.
In short a VPN removes a key personal identifier that can be used to ID you online. Your IP address.