My ADSL router/modem's box lists "NAT firewall" as a feature. Do I need a separate software firewall? And if I do, what is this NAT firewall thing good for?

NAT stands for network address translation. It is used by the router to redirect data from the internet to the appropriate computer inside the router's network, as well as redirect data from an inside computer to the router to the appropriate computer on the outside.

Sounds like they're throwing in all the buzzwords they can. It's probably just an integrated firewall.

And would an integrated firewall mean I don't need a separate software firewall?

It would as far as my common sense is concerned, but you never know with these tech things.

By the way, I just remembered there's a tech forum...

As The_Mega_ZZTer said NAT isn't a security feature, but for communication. A firewall would be a packet filter. They could mean that with NAT firewall. What brand/model is your router?
But as long as you aren't running any useless services you should be secure. If you still want a firewall running on your own computer, WinXP's own firewall is all you need.

It's an A-Link Roadrunner 44C.

It kinda is a security feature, but not by design I think. Though if your NAT-ing box has no firewall on it, you might lose it pretty quickly and there goes the security.