NAT is a common technique often used to allow multiple computers to transparently (mostly) share an internet connection. When the computer performing the NAT (often known as a NAT box, name explained later) routes the systems behind it onto the internet, it transparently changes the source IP address of the internal system to it’s external (Internet) address and remembers basic data about the connection. The packet then traverses the internet to it’s destination as if it had been generated by the “NAT box” itself. When the reply is sent back, the “NAT box” looks at the connection tracking data it stored before and determines where to send it back on the internal network. To the computers on the local network, the “NAT box” looks like just another router hop, but in reality, it is doing all sorts of magic.
The term “NAT box” stems from the functionality is has, that being NAT. In NAT, or Network Address Translation, the network address is being translated at the router. This is what creates the illusion of only using 1 IP.
The benefits of NAT are great. It allows many computers to access the internet utilizing only a single IP address on the internet. This not only saves money for the organization employing NAT, but also conserves addresses on the internet as few are still avaialble.