NAT is short for Network Address Translation.
In a nutshell, NAT allows a group of computers to use a single IP address to communicate with the outside world or another network. Additionally it separates External IP addresses from Internal network IP addresses.
A device or program using NAT sits between the Internet and the network. It rewrites IP addresses and port numbers on the fly so every packets appears to be coming from (or going to) the single IP address of the NAT device instead of the actual source or destination. This allows more then one system to access the Internet at the same time, and it allows a measure of safety as the outside site never sees the internal IP address for the system it's sending to. In this way, NAT also acts as a simple firewall.
