The feature set of fine grained access control, simple user groups, GUI editor, easy install, simple but efficient spam protection, easy theming combined with a simple code base makes it often the wiki of choice for many open source projects (e.g. Apache, Debian, Ubuntu, Fedora) and corporate wikis.
MoinMoin's storage mechanism is based on flat files and folders, rather than a database. This makes it easy to manipulate the content in a text editor on the server if need be, including managing revisions if the wiki gets attacked by spammers. A storage abstraction layer is currently being worked on, which will allow the server administrator to select between flat file-storage or a relational database.
MoinMoin supports plugins and can be extended via Macros and Actions. It also uses the idea of separate parsers (e.g. for parsing the wiki syntax) and formatters (e.g. for outputting HTML code) with a SAX-like interface between the two. The idea is that if you want to be able to output DocBook instead of HTML, you only need to write a docbook-formatter that implements the formatter interface, and all parsers that use the interface will automatically be supported.
MoinMoin uses CamelCase linking by default, but also has support for non-CamelCase linking.
MoinMoin also has extensive support for Access Control Lists that greatly increase its usability in a content management system. It also has GUI editing capabilities, and the upcoming 1.6 version is able to search also in attachments.
1.6 will also allow synchronisation of contents from instance to instance via XML-RPC and therefore allows distributed offline editing on a laptop, mostly done via the desktop version of MoinMoin.