Let me clarify what Sayo said a bit. Your router will connect you to the internet, and your ISP will assign you an IP to use for your connected session. This IP is available to everyone on the internet; they can connect to it and reach you from anywhere, so we can effectively call it an external address.
However, on your actual internal network itself, you can have many computers. So on each of these computers, you can assign an internal ip address; that is, ips that you can connect to from your local network only. In my case, I use 192.168.0.1 as my router address, 192.168.0.2 as my computer, 192.168.0.4 as my server and a few others. So effectively the router "routes" internet traffic from your computers to the internet, but shields people from connecting externally to one of your computers. This type of networking is called a VPN.
Have a google for port forwarding, this might help you a bit.