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.