Why is NAT Important ?
Solving the shortage in Address space
With NAT it is possible to share a single address between multiple computers and connect them all the same time to the Internet. Moreover; users who do not require external communication with the outside network (Internet) do not consume public IP addresses.
Growing Concerns Over Security
NAT did not only offer a solution for the increased demand and cost of IPv4 addresses, but also improved the overall security of networks by forming a first line of defence against external attacks. The main idea was to set up individual private networks that are connected indirectly to the Internet, NAT routers will translate the addresses in the datagram from the private network to the public internet and vice versa. [ More on Security ...]
Ease of Administration
Maybe one of the main reasons NAT is widely spread is because it provides the ability to manage and monitor the network on a large scale, administrators can still enjoy the control benefits that come with a private network and still be able to connect to the Internet, it is easy to add clients and even change the main Internet service provider as the change will only happen on the public addresses. [ More on Administration ...]