Your public IP is what every website, service, and app you connect to sees by default. It's used for rough geolocation, access restrictions, and can be tied back to your ISP account. Proxies and VPNs work by having a server make requests on your behalf, so sites see the proxy/VPN's IP instead of yours.
Curious whether an IP is flagged as a proxy or VPN? Try our Proxy/VPN Detection Checker.