Network Address Translation, or NAT, is a process in which home or office internal computers can use the Internet in a private and secure manner. Home Firewalls use NAT almost exclusively as their firewall mechanism. All of the internal computers will use an IP Address range of something like 192.168.1.2 and the Firewall would attain the public ip address that is assigned by your ISP.

When an internal computer wants to access the Internet, the Firewall will translate the internal computers address to the public address given to the Firewall.

An example would be if your home computer has an IP Address of 192.168.1.2 and your router would have the public IP Address of 66.65.94.12. When you connect to a website your internal address of 192.168.1.2, would be translated to the public address of 66.65.94.12, making it seem to the web server that you were coming from the 66.65.94.12 address and not the 192.168.1.2 address.