The nat is Network Address Translation that your networking devices use. This can be open, moderate, or strict (in descending order of quality). Your NAT determines who you can chat, play, and message.An open NAT being the best, is what you want. An Open NAT means you can join/ play with anyone on any network. A moderate NAT only allows you to play with people on an open and moderate network. A strict NAT plain and simply sucks.
Currently about a third of the users of xbox live have this issue and it would greatly help if people would fix it. To fix it you'd either need to call your router or IP provider and have them help you open your firewall ports through your computer. These ports are the UDP 88, the UDP 3074, and the TCP 3074 port. This should fix the problem.