The DNS system does only three things: it translates hostnames (www.forest.net) to IP addresses (216.168.37.138), IP addresses to domain names and directs where mail should go for a domain. It does this via text-based lookup tables that list hostnames and the associated IP addresses and mail routing information.
Each domain name must have at least two nameservers (a primary and a secondary) to be visible to the Internet. These nameservers answer questions about the domain (i.e.: what is the IP address of www.forest.net?) to the Internet community.
The InterNIC, currently run by Network Solutions, assigns or delegates which nameservers answer for which domains. They run what are called the root nameservers, which is the master list of domains and the nameservers that have been delegated to host them.
If a domain is not in the root nameservers, it does not exist for all practical purposes. Domains are only added by registering new domains.