An IP address is critical to network communication. It's kind of like a telephone number; it's how computers know where to send data from one point to another.
NAT stands for Network Address Translation. In the context of our network, NAT is how one (public) IP address is turned into many (private) IP addresses.
A public IP address is an address that is exposed to the Internet. If you search for "what's my IP" on the Internet, you'll find the public IP address your computer is using.
If you look up your computer's IP address using the tools provided by the operating system, you'll see a different IP address: this is your device's private IP.
Chances are, if you check this on all of your devices, you'll see that all your devices are using the same public IP addresses, but all have different private IP addresses. This is NAT in action. The network hardware uses NAT to route traffic going from the public IP address to the private IP address.
NAT is important because the Internet Protocol that most of the world uses, IPv4, only has so many IP addresses that it can use: 2^32 or 4,294,967,296 to be exact. That may sound like a lot, but there is not enough for each device every person owns to have their own public IPv4 address. NAT is essential for the entire Internet to work.
Our system has the capability to create what is called a bidirectional NAT for individuals who want access to their own public IP address. These IPs are available for purchase (availability varies) and create a 1-to-1 relationship between a private and public IP address.
Chances are, if you don't know why you would need this public IP, then your probably ok just using NAT. However, some gaming devices work better when they have access to a public IP. For more information, see this article.