From a DNS perspective, an administrative domain is a group of machines that are administered as a unit. Information about this domain is maintained by at least two name servers; they are "authoritative" for the domain. The DNS domain is a purely logical grouping of machines. It could correspond to a physical grouping of machines, such as all machines attached to the Ethernet in a small business. But a local DNS domain just as likely could include all machines on a vast university network that belong to the computer science department or to university administration.
For example, suppose the Ajax company has two sites, one in San Francisco and one in Seattle. The Retail.Sales.Ajax.com. domain might be in Seattle and the Wholesale.Sales.Ajax.com. domain might be in San Francisco. One part of the Sales.Ajax.com. domain would be in one city, the other part in the second city.
Each administrative domain must have its own unique subdomain name. Moreover, if you want your network to participate in the Internet, the network must be part of a registered administrative domain. The section "Joining the Internet" has full details about domain names and domain registration.