DWiki stands for 'Dinky Wiki', which is what ChrisSiebenmann calls this for lack of a better name. As far as Chris knows on a casual scan, 'DWiki' is not being used as the name of any other Wiki software.
I (ChrisSiebenmann) wrote DWiki to have a good environment for writing documentation about how we do system administration work on our Unix systems. You can see a bigger list of Features if you want.
DWiki's design choices are very slanted towards making it as easy as possible for us to write, revise, and maintain system documentation. (Because on past evidence, it if isn't dirt easy we just aren't going to do it.)
I like WikiText, because it is a simple, low-effort way to write documentation that comes out looking decent. But I don't like the wiki interface for writing it: web browsers make crappy editing environments and limit the sort of changes you can easily do. So I wrote DWiki to have a good system for displaying wikitext that we'd write through other means.
Some people say (strongly) that DWiki is not a Wiki because people (currently) can't edit DWiki pages over the web; they argue that instead it should be called a CMS (a (web) Content Management System).
I'm willing to accept this argument in theory, but ...
I like punchy, usefully descriptive names. My personal opinion is that 'wiki' is one: calling DWiki a wiki tells you a great deal about it, while calling it a CMS tells you almost nothing.
So while I may be willing to accept the argument, DWiki stays being called a wiki (and keeps the 'Wiki' in the name).
I maintain web-based editing makes little sense for us, and wrote a bunch about why in WhyNotWebEditing.
And one can always have a big debate over at the granddaddy Wiki, at http://c2.com/cgi/wiki?WikiPrinciples.