See your router's instruction manual or contact your ISP for a detailed explanation. The router also has its own local/private IP address in addition to the external/public IP address.
This process is known as Network Address Translation (NAT) or IP Masquerading. These local or private IP addresses can only be seen from your network and are usually of the form .x or 10.0.x.x. The router uses this address, but the router allows your Macs to have one or more local or private IP addresses. This is your external or public IP address. Most Internet Service Providers (ISP's) supply a single internet address for you to use.
Unfortunately, this often causes problems for hosting internet games (both with GameRanger and without). The main purpose of a router is to share your internet connection across multiple computers. If you have a broadband internet connection (and in some cases, dialup modems) chances are your Mac is behind a router. Read about the Network Changes if you haven't already. In the majority of cases, port forwarding is no longer needed.