NAT (Network Address Translation) allows private IP addresses to be translated to public IP addresses to allow access to the internet. There are three types of NAT: static NAT maps a single private IP to a single public IP; dynamic NAT maps multiple private IPs to multiple public IPs; and PAT (Port Address Translation) maps multiple private IPs to a single public IP by multiplexing ports. The document provides configuration examples for static NAT, dynamic NAT, and PAT on Cisco routers to translate private to public IP addresses and allow internal hosts to access the internet.