What is TWiki? Officially, it is a "Enterprise Collaboration Platform" (yawn). What that means is that it is a wiki software that is meant to be used for intranet information.
I've used it minimally so far mainly because it looks ugly, but I see that the official latest version has improved by leaps and bounds. I have started to use it quite extensively.
Some of the things I like:
Reasonably clean formatting rules - This factor can never be emphasized enough. TWiki's rules are heck of a lot better than other wiki syntaxes I've come across (including MediaWiki's).
Help section is to the point.
The list of plugins just makes me go wow.
Discussions are integrated into the pages like the page on StructuredWiki (our older version still doesn't :| )
There's a presentation that gives a good introduction to TWiki.
Aside: I wonder what tools other companies/organizations use.