Network Address Translation (NAT):

In computer networking, network address translation (NAT) is the process of modifying network address information in datagram packet headers while in transit across a traffic routing device for the purpose of remapping a given address space into another.
Most often today, NAT is used in conjunction with network masquerading (or IP masquerading) which is a technique that hides an entire address space, usually consisting of private network addresses (RFC 1918), behind a single IP address in another, often public address space. This mechanism is implemented in a routing device that uses stateful translation tables to map the "hidden" addresses into a single address and then rewrites the outgoing Internet Protocol (IP) packets on exit so that they appear to originate from the router. In the reverse communications path, responses are mapped back to the originating IP address using the rules ("state") stored in the translation tables. The translation table rules established in this fashion are flushed after a short period without new traffic refreshing their state.
As described, the method only allows transit traffic through the router when it is originating in the masqueraded network, since this establishes the translation tables. However, most NAT devices today allow the network administrator to configure translation tables entries for permanent use. This feature is often referred to as "static NAT" or port forwarding and allows traffic originating in the 'outside' network to reach designated hosts in the masqueraded network.
Because of the popularity of this technique, see below, the term NAT has become virtually synonymous with the method of IP masquerading.
Network address translation has serious consequences (see below, Drawbacks & Benefits) on the quality of Internet connectivity and requires careful attention to the details of its implementation. As a result, many methods have been devised to alleviate the issues encountered. See article on NAT traversal.