It's the address websites see when you visit them: your router's or your mobile network's, not your device's address on your own network.
Copy next to an address copies it, and Check again looks them up again, for example after turning a VPN on or off.
IPv4 and IPv6
IPv4 addresses look like 203.0.113.7, IPv6 ones like 2001:db8::7. Many connections have both, and the browser picks one for each site, usually IPv6. The one it picked here is marked used for this site.
Each is looked up on its own, so you see both. Blocker extensions often stop these lookups as tracking; then the address is found over WebRTC instead, the way video calls find theirs.
"Not found" means neither answered: your network may not have that kind (many have no IPv6 yet), or something in your browser or network stops both.
Details
Country is where your address is registered, which is usually, but not always, where you are. A VPN shows its own country.
Network is who your address belongs to, usually your internet provider, with its AS number. With a VPN, it's the VPN's network. Hostname is the name your address has in reverse DNS; many have none.
Clock compares your device's clock with Cloudflare's: a wrong clock breaks sign-in codes and secure connections. Connection shows the HTTP and TLS versions, and whether the key exchange is post-quantum.
Cloudflare data center is the nearest Cloudflare server that answered, by its airport code (IST for Istanbul, FRA for Frankfurt). Cloudflare WARP shows only when Cloudflare's VPN app is on.
Copy all copies everything as text, for example for a support request.
Privacy
Your addresses are looked up through Cloudflare, which already carries this site's traffic: on this site, on Cloudflare addresses that answer only over IPv4 or only over IPv6, and, when those are blocked, on Cloudflare's STUN server.
The network and hostname are asked through Cloudflare's DNS: the network in Team Cymru's public IP-to-network list, the hostname in your provider's reverse DNS. They see your address in the question, but not who asked.
Nothing is stored, and nothing is sent anywhere else.
What's My IP
Your public IP address as the internet sees it, IPv4 and IPv6, with your internet provider, country and connection. Nothing is stored.