You might know the fact that internet size is doubled each year. It means number of users are increasing with a rapid rate. This increasing rate of users is the main reason behind introduction of Network Address Translation.
You know that IP address is required to connect one computer to the web servers and other computers. This IP address is a 32 bit number. IP address contains address or location of any computer. The number of available IP addresses are smaller (about 3.2 billion). In the near future this size will not be sufficient to match with number of computers. IPv6 is a solution to this problem but it will take time to implement. Here comes Network address translation into play. By using this technology a unique IP address is required for a group of computers.
NAT also makes your network safe by hiding your home computer behind your router. Your assigned IP address is assigned to NAT router and then the router assigned its internal IP to computers in the home network which makes it impossible for external computer to figure out your home network.
If you want to know more about this technology then check out this guide by HowStuffWorks.