Basically, you have:
Router:
Internal IP - 192.168.0.1
External IP (Static IP/One from ISP): 4.2.2.1
Server:
IP - 192.168.0.2
Now in this example you want to set up a web server, so anyone going to 4.2.2.1 gets to the web server on your server in your house (192.168.0.2).
To do this, on your router, you need to set up port forwarding so that TCP port 80 is forwarded to 192.168.0.2:80 (Port 80 on 192.168.0.2). Your router will then use Network Address Translation/Port Forwarding to pass through the traffic from the outside to the inside while tracking the TCP connection to keep it alive.
HTH.