Developers are the people contributing to the code of MediaWiki software. They commit changes to the central Git repository by pushing changes for review in Gerrit where the latest copy of the software is stored. Developers include paid Wikimedia Foundation staff and volunteers. Anyone can submit a patch for review after creating a developer account (but only maintainers can merge it). To see which developers are actually active, try https://www.openhub.net/p/mediawiki/contributors, which gives nice stalkerish summaries of all sorts of fun statistics.
Developers are not to be confused with system administrators, who are people having shell or root access to Wikimedia Foundation servers, where the code repository is stored. They might not really be developers; in many cases they rarely use their commit access, or if they do, only to maintain non-MediaWiki things in the repository.
A maintainer of a specific project (including MediaWiki core or a extension) has +2 access to the relevant Git repository, so that they can merge patches others submitted. They usually regularly respond to bug reports and changeset review requests. A list of maintainers are kept at /Maintainers.
Historically, developers also manage Wikimedia Foundation servers (now managed by system administrators). Before bureaucrat and steward groups are created, they are the only ones able to promote and demote sysops, and lock user accounts (before the "block" feature of MediaWiki existed). Thus they had an important role in the Wikipedia power structure.
From April 2006 to March 2012, Subversion was used. Only people with Subversion commit access (which must be approved by SVN administrators) can submit codes. Codes submitted to Subversion are merged to MediaWiki codebase immediately (though only be manually deployed to Wikimedia wikis by a system administrator), and may be reviewed by "coders" before they are deployed. In January 2013, the MediaWiki SVN repository was made read-only. All active projects have moved to Git.