MediaWiki is the software that most wikis (including All The Tropes) run on, and it is a play on the name "Wikimedia" (as in the Wikimedia Foundation).
In fact, MediaWiki was designed by Wikimedia Foundation to replace UseModWiki, the software Wikipedia initially used until its limitations quickly became apparent. They created a new wiki engine that was written in the PHP scripting language with a MySQL database backend, designed for hosting a community-based encyclopedia project (or any large-scale wiki project in general).
MediaWiki is licensed under the GPLv2 license and can run on multiple platforms. It is free software that can be modified by anyone for any purpose, and it generally tends towards open source data formats, and its licensing terms were chosen to reflect this. It also allows for easy creation and installation of add-ons and extensions for expanded and/or specialized functionality.
The most well known MediaWiki wiki would be the Wikimedia Foundation's flagship wiki, Wikipedia, from which other projects such as Wiktionary, Wikinews, and Wikibooks were designed as spinoffs. MediaWiki is also used by many companies for writing help documentation, used by Wikia (in a heavily modified format) to host wikis of all varieties, and can be used by practically anyone to host a wiki for any purpose one can dream up.
- Wikipedia Syntaxer: Wikipedia was the first MediaWiki site, and much of MediaWiki's syntax dates to the UseModWiki and Phase II software that preceded MediaWiki.