The way NAT works is it is given a public IP address it uses to communicate with the public network. The NAT will have a port mapped to each host behind it, which can have IP's in the range 10.x.x.x or 192.168.x.x, and any servers in the public network communicate with those hosts through the NAT, by sending the packets to the NAT's IP address and the port the NAT has associated with the host. Depending on the type of NAT used, it can let any packet through so long as it is sent to the correct port, or it can only allow packets that are sent to the correct port and from the correct source IP and source port.
Another purpose of NAT is to act as a form of firewall.