Original: 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.
Simplified: Such kind of firewalls use translation tables to map the "hidden" addresses into a single address and then rewrites the outgoing IP packets on exit from the router so that they appear to originate from the router.