Xbox LIVE will define NAT as three specific types; Open, Moderate, Strict. To determine your current NAT setting you'll need to use the "Network Troubleshooter" which is located by going to the following screens:
Select "My Xbox" and then select "System Settings"
Select "Wired Network" or the name of your wireless network, if you are prompted to do so.
Select "Test Xbox LIVE Connection"
Depending on what your NAT type is will determine whether or not you will be able to join or host a specific multiplayer game.
As shown in the table above, Xbox LIVE will allow consoles with Open NAT Types to connect to both moderate and strict connections. Strict connections however can only connect to Open NAT types. Basically this means if you're current NAT type to the Xbox LIVE network is showing up as Strict you will only be able to join games for those connections that have Open NAT types.
If you've received a NAT warning from either the Network Troubleshooter or from within any of our games there are some possible solutions that might help solve resolve this issue. (These 3 solutions can also be found at the Support section of the Microsoft website located here)
Solution 1 - Turn on UPnP on your network hardware:
Universal Plug and Play (UPnP) is a standard that helps routers communicate effectively. If your router or gateway supports UPnP, make sure this setting is turned on. Please refer to your hardware documentation for help turning on UPnP. Most hardware manufacturers have websites that include support information. If you change the UPnP setting on your network hardware, restart your hardware and test your Xbox LIVE connection.
Solution 2 - Simplify your setup:
Your router or gateway might be having problems sharing an Internet connection. To see whether this is true, try simplifying your setup. If you have a wired connection: Temporarily unplug everything from your router, except the cable to your modem and the cable to your Xbox 360 console. or If you have a wireless connection: Temporarily turn off everything that's connected to your wireless network except your Xbox 360 console. Test your Xbox LIVE connection. To do this: go to My Xbox, select System Settings, select Network Settings, select Wired network or your wireless network name (if you are prompted to do so), and then select Test Xbox LIVE Connection. If you do not receive a NAT warning after simplifying your setup, it suggests that the router is having problems handling multiple connections. To try to fix the problem, please go to the next solution.
Solution 3 - Open network ports:
Your network hardware or firewall might be blocking communication with the Xbox LIVE servers. If you're connected to a network through your workplace or a college, ask the network administrator to open the following ports:
If you're not connected to a workplace or college network, you need to open network ports on your network hardware. For more information on how to open these ports please visit the Microsoft Support Site, located HERE.
For more information about NAT types and a detailed explanation for each type and how it connects to other machines please visit the Official Engineering Blog at Xbox.com located HERE.