A
domain you register for the sole purpose of
having your own domain so you can have an easily remembered
URL and
e-mail address. The domain is usually served
(often
vhosted) off someone else's machines.
This is as opposed to a domain you register because you have
machines of your own which are already on the Internet and
which you want to make addressable via something other than
dot addresses.
Whereas vanity domains were almost unheard-of in 1980s, since
the invention and popularisation of the
Web in the mid-1990s
and the desire for URLs which consist only of memorable
domain names (e.g., "http://pbs.org") for everything from
movies to car wax, vanity domains have come to be the rule
instead of the exception.