NAT is network address translation.
https://en.wikipedia.org/wiki/Network_address_translation
The following shows a nice guide on how to do it for xbox 1
http://www.entertainmentbuddha.com/how-to-get-an-open-nat-on-the-xbox-one-for-better-connections/
The first thing you need to do is to give your xbox an ip address that can't change, a static IP.
This can either be done on the device or on the router.
The guide shows how to do it on the device itself.
Then you would open ports 3074, 88, 80, and 53 for the ip address of your xbox 1 that you just set.
If they ask for any of the following these values should work;
Subnet: 255.255.255.0
DNS1: 8.8.8.8
DNS2: 8.8.4.4
Gateway: the ip address of your router, you can find this by typing
ipcongfig -all
in a cmd box. This is the Ip you connect to change router settings.