Domain Name Service is one of the most critical, and also one of the more complicated, Internet services. It provides the ability to translate human-readable symbolic names into IP address numbers (and also numbers back into names). Understanding how DNS works is critical to managing and troubleshooting many other service problems.
Almost all other Internet applications are DNS clients because they have to look up IP numbers from hostnames to make connections, which is why reliable DNS is critical. DNS provides a number of built-in redundancy and reliability features. Few administrators, however, tend to run DNS servers, usually because the only ones who need to do so are in organizations that own their own domain names and have the need to frequently add or remove names under those domains. DNS servers must also be delegated and registered to be effective as public resources, limiting the number of people who can run them.
The naming hierarchy in DNS is a n-way tree whose top level is an unnamed root (although it can be referred to as '.' "dot"). Underneath the root are the "top-level" domains -- com, edu, gov, mil, net, org, some other more recent additions like biz, info, museum, and the "country-code" domains based on ISO two-letter country codes such as jp, de, ca, br (and over a hundred more). There is also a special arpa top-level domain with a subdomain in-addr which is used for "reverse DNS" (described later). Under these top-level domains entities called "registrars" allocate and delegate "second-level" domains to organizations, and those organizations provide the DNS for those domains and can sub-delegate the domains they manage to arbitrary depth.
As an example, our lab domain ilab.cs.uoregon.edu is delegated to a name server in the lab run by me while our class is in session. cs.uoregon.edu is delegated to them by U of O Network Services who manages the servers for uoregon.edu. The registrar Educause (educause.edu) delegates uoregon.edu to the U of O.
A "zone" or "zone of authority" is some subtree of the DNS space served by a particular server. That server may delegate sub-subtrees to other servers, which then take over those regions as their zones.