Right.. NAT (Network Address Translation) allows the router to adopt the IP address scheme from the modem and then use an internal non-routable private ip scheme for the rest of the network.
Most IP schemes used are in the 192.168.1.0 or 192.168.0.0 range.
NAT is useful because you can have multiple computers accessing the internet via a broadband service and to those of us on the internet it will appear as only one computer is connected because all traffic will be routed through one IP.