NAT (Network Address Translation) is what your router does to route IP packets from the outside world ('internet') to your local (LAN-side) network, and visa versa. Basically, it changes the IP address in the IP packet headers. Routers generally run some-unix-distribution-or-other as their Operating System and often have BUGs in their network stack. So it sounds like you ran into a software BUG in your router firmware which will require a reboot to correct.
(edit: sorry, this was actually a response to the first reply in this thread which I'd thought was the OP)