A wiki is a type of website whose contents can be edited from the web browser, and which keeps a version history for each editable page. Wikis are often, but not always, editable by any visitor to the site.
Definition of a Wiki taken from Media Wiki page on the Differences between Wikipedia, Wikimedia, MediaWiki, and wiki
Wikimedia is the collective name for the Wikimedia movement, revolving around a group of inter-related projects, including Wikipedia, Wiktionary, Wikiquote and others, which aim to use the collaborative power of the Internet, and the wiki concept, to create and share free knowledge of all kinds.
Definition of Wikimedia taken from Media Wiki page on the Differences between Wikipedia, Wikimedia, MediaWiki, and wiki
The mission of the Wikimedia Foundation is to empower and engage people around the world to collect and develop educational content under a free license or in the public domain, and to disseminate it effectively and globally.
In collaboration with a network of chapters, the Foundation provides the essential infrastructure and an organizational framework for the support and development of multilingual wiki projects and other endeavors which serve this mission. The Foundation will make and keep useful information from its projects available on the Internet free of charge, in perpetuity.
Mission statement as fouind on the Wikipedia Mission Statement page.