DocsApp is the application that serves up this documentation. It's custom-built in PHP using the Slim Framework, with a local SQLite database to index the search, translations and contributors. It's also open source, and contributions are more than welcome! :)
If you'd like to improve the documentation site (rather than the content), start by reading the DocsApp Readme.
The documentation at https://docs.modx.com is hosted on a MODX-sponsored server. The mirror at https://docs.modx.org is hosted on a modmore-sponsored server and occasionally used as a staging environment for new features or improvements.