Learn to port forward your Belkin F9K1113 router in under 5 minutes with our simple to follow directions. We show you how easy it is in 4 simple steps.
portforward.com
Other games might use miniupnp to set up ports which is an automatic way to do it. If you set up your PC on the Internet it would have probably worked, but it's very unsafe. Also keep in mind that your public IP can change from time to time because ISPs don't want people running servers. If you wanted to set this up long term, you'd need to use a dynamic DNS server like No-IP.com. Dynamic DNS services have a client you run that will update a No-IP DNS server to translate your friendly minecraft servername (ie, "bobsminecraftserver.no-ip.com" to whatever your current public IP address is.
Port forwarding in your router is how your router knows to send inbound traffic from a port to an internal computer. It will route all port 25565 traffic to your internal computer's IP. It's safer because only that port (25565) is exposed to the Internet.
If you do that telnet test from the computer you're running the server it's on will tell you if the minecraft server service is running and answering traffic on 25565. It won't tell you if your minecraft server computer is accessable outside of the computer (your firewall could be blocking, but testing on the local machine wouldn't show you). That's why you should test from a computer inside your network that is not the minecraft server. You need to test to see if it's working in steps...
1) Telnet to 192.168.0.10 (or whatever your internal IP is) port 25565 on the server itself to test if the software is running and answering 25565 requests.
2) Telnet to 192.168.0.10 (or whatever your internal IP is) port 25565 from another internal computer to test that your minecraft server is available outside of the server.
3) Telnet to (public IP address) port 25565 from a computer on the Internet to verify your port forwarding is working.