The domain in Windows NT/XP is a special and unique concept, so it's hard to define it as anything other than "domain". Basically, at its core, XP is a network-based operating system, and all computers on this virtual network have a "domain" which allows a sense of organisation. Sometimes XP has trouble connecting to that virtual network.

Directly from the XP manual I have: "a collection of computers on a network, sharing common information that is managed by a network administrator".

To be honest, I still don't even really understand the concept myself.

The full term for "domain" is "Active Directory domain". AD is great fun. We use it at work. It's just a way of administering a network of Windows PCs. Logins are handled by AD, which allows users to roam from one computer to another and still have their login work (along with their home directory, which is mapped to a share on the file server, and some of their settings).

You can enforce global policy settings on the domain; for example, enforcing a particular Automatic Updates setting*, or securing computers in some way. You can set login scripts and this kind of thing. It has literally dozens of features.

*At work we run a WSUS server, which downloads Windows patches from Microsoft and then distributes them to other computers. A group policy setting is used to force the computers in the domain to get their updates from the WSUS server. No sense downloading the same data over the internet 100+ times when we could just serve it locally! We pay for bandwidth.