MediaWiki is a collaboration and documentation platform brought to you by a large community. It is the software that powers Wikipedia and helps you collect and organise knowledge and make it available to others. It is multilingual and can be extended with extensions. You download, install and configure MediaWiki yourself on your own server, including a database; stable, legacy and long-term support (LTS) releases are available. If you do not have a server, the project site lists hosting services, and there are parties offering professional development and consulting.
The Wikimedia Foundation, a non-profit organisation headquartered in San Francisco, runs the Wikimedia projects and the MediaWiki software. The software is released under the GNU General Public License. Because you can install MediaWiki yourself, you decide where the data resides; there is no mandatory cloud run by the developer. If you choose an external hosting service, the location of your data depends on that provider, and MediaWiki itself is not involved.