I tried looking up "domain" in the index of several of my Vista books,
no luck.
The concept of a "domain" is a networking one, and doesn't pertain to
Vista in particular. That's probably why you couldn't find it in your
books.
It's somewhat of an oversimplification, but a domain is a network that
uses a server, rather than having all computers be equal, on a
peer-to-peer basis.
Domains are used almost exclusively by large
organizations--businesses, governments, and Universities--rather than
in home environments.
One of the advantages of Vista Ultimate is that it is supposed to handle
domains better than other versions of Vista.
What does that mean?
Vista editions come in two categories--the Home ones (Home Basic and
Home Premium) and the "Professional" ones (Business, Enterprise, and
Ultimate). The ability to join a domain exists only in the
Professional editions, not the Home ones (not surprising, because, as
I said, few home users have any need of domains). But all three of
those Professional editions (Business, Enterprise, and Ultimate) have
equal support for domains.
Be gentle, I have just started using windows so do not know my way
around yet, as all my previous experience is with Macs.
I've answered your question here, in this Windows XP newsgroup, even
though you asked about Vista, because a domain pertains to Vista and
XP equally. But for the future, please ask Vista questions in a Vista
newsgroup instead.