NAT (network address translation)
NAT lets many devices share one public IP address by rewriting packet addresses at the router; it is why your local IP differs from your public one.
What NAT is
Network address translation is what a router does to let a whole network share one public IPv4 address. Devices inside use private addresses from ranges such as 192.168.0.0/16 or 10.0.0.0/8, which are never routed on the internet. When a device sends a packet out, the router replaces the private source address with its own public address and remembers the mapping, usually keyed by port number. When the reply comes back, the router looks up the mapping and forwards the packet to the right inside device. From the outside, every device in the house looks like the router.
Carriers do the same thing one level up. Carrier-grade NAT puts thousands of subscribers behind a single public address, using the shared range 100.64.0.0/10 between the customer router and the carrier's translator. Most mobile connections and a growing share of home connections work this way.
Why it matters
NAT is the reason the address your computer shows in its settings is not the address websites see. It is also the reason that inbound connections do not work without port forwarding: the router has no mapping for a packet nobody inside asked for. Peer-to-peer applications work around this with STUN, which is how WebRTC learns a public address and, as a side effect, how a web page can discover the address behind a browser proxy.
For reputation, NAT means an address is shared. One abusive user behind a carrier's translator can get the address listed on a blocklist for everyone else, and that is also why sites are cautious about blocking mobile and large residential addresses outright.
IPv6 removes the need for NAT by giving every device a global address, which is cleaner for connectivity and worse for the "hide behind the router" effect many people have come to rely on.
How to check
IP lookup shows your public address as websites see it; compare it with the address in your operating system's network settings to confirm you are behind NAT. The WebRTC leak test shows the addresses the browser discovers through STUN, and the port checker tests whether a port on your public address is reachable from outside, which tells you whether a forwarding rule is working or whether a carrier translator is in the way.
A common misconception
NAT is not a firewall and not a privacy feature. It blocks unsolicited inbound packets as a side effect of having no mapping, but it does nothing to hide outbound traffic, and the public address still identifies your household or your carrier gateway.