Each host has a unique address, which is given as a dot separated list of named domains. For example:
ftp.ucs.ed.ac.uk
This is the "domain name" of the host which acts as the anonymous ftp server (ftp) for the university computing services (ucs) at Edinburgh (ed). As a university it resides in the academic (ac) domain for the United Kingdom (uk).
You might not need to give the full address. In the above example, someone at another UK academic site only needs to use the ftp.ucs.ed part of the name. They can assume that their local host is in the same (academic) domain as this host.
Names can also be given as a series of dot (.) separated numbers. For example
129.148.31.66
can be used instead of
wilma.cs.brown.edu (66) (31)(148)(129)
Each number is the identifier for a particular domain. However, unlike domain names, the left-most number is the most significant, and represents the top domain.