The kinda dumbed down (no offense to you) explaination is that it fools your xbox into thinking it's in a system link LAN game (like hooking up 4 xboxs to a hub or switch) and directly connecting to other xboxs.
What XBC/Xlink/Gamespy do is grab the packets from the game - most famously halo - and transmit those across the internet to whomever else you're playing with. So it's essentially playing in a LAN online? Kinda weird if you think about it but that's what the xbox is doing with the help of XBC.
Download XBC, create your username etc and login
You'll want to find your xbox in it's options (should have instructions there) and all the appropriate network configs are on their site -I believe my signature's links are still active I need to check up on that.
Once it's found you just join a game room above the chat area (choose a low ping'd one) and go to System Link on your Halo and you should see the game pop up