"Network Address Translation" is a method for translating the (mostly private) IPv4 addresses of a network onto other (mostly public) IPv4 addresses of another network.
NAT therefore enables several PCs in an LAN on the one hand to use the IP address of the Internet Access Router for Internet access and on the other it hides the LAN behind the IP address of the router registered on the Internet.
NAT therefore spares the need for each user to have a separate provider contract.
If, then, the client in the LAN sends an IP packet to the router, NAT converts the address of the sender into a valid IP address, which for instance has been assigned to it by the provider, before it is passed on onto the Internet.
If an answer to this packet comes back from the remote station, the NAT converts the receiver address back into the original IP address of the local station and delivers the packet in proper form. In theory, NAT can manage LANs with any number of clients.