When testing your Internet connection, you may be told you have a connection issue in the form of your NAT or Network Address Translation type.
In a typical home situation, multiple Internet-enabled devices are connected to the Internet via a router. While those multiple devices all have Internet access to the outside world, all of these actually appear as one device, the router itself. When your router receives data from the Internet, NAT ensures that the information intended for, say, your Xbox 360, ends up at the Xbox like it's meant to, and not your PC.
According to the Xbox 360, there are three NAT types that your router may be set to: Open, Moderate and Strict. If your NAT type is Open, your home network is set up to best support Xbox Live and other people should have no issues connecting to you. If your NAT type is Moderate, you might have problems connecting with other Moderate or Strict users.
If your Xbox 360 identifies you as having Strict NAT, you'll likely be able to talk only to those who are on Open connections, and perhaps some Moderate, but they may have problems connecting to you.
There are a few methods you can employ to improve your NAT rating. Firstly, see if your router supports Universal Plug and Play (UPnP) in its settings. If it does, make sure this option is turned on in the router's Web interface--this should simplify the implementation of your network and help with your NAT issue.
If you're a bit more technically minded and you still have an issue, you might need to clear your router's firewall and set up port forwarding properly, sometimes called "virtual server". To do this, you'll need to know the IP of your Xbox 360, and you'll need to either open these ports in your firewall, or point them toward your Xbox 360's IP. Unfortunately, every router is different so you'll have to find the appropriate settings on your own.
If technical stuff scares you and you're still pulling your hair out, as a last ditch option, you could try disconnecting or turning off any other devices that are also attached to your network such as laptops and other gaming devices. This may give priority to your Xbox and help address the problem.
Finally, if you are in the market for a new router and don't wish to encounter this problem, try looking for one that is marked as being compatible with Xbox Live or Windows Vista--these models have been tested to work well with Xbox and other Microsoft systems.