There are several versions of MediaWiki available for download at any given time. Extensions also can have various release statuses.
The development version is available by downloading from Git the trunk. It is generally quite stable, and there are some wikis that run from the trunk.
The beta version has been reviewed and is thought to be good. It is more stable than the trunk. However, you are encouraged to report any bugs you encounter to Bugzilla, so that they can be fixed for the officially stable version.
The stable version is even more stable than the beta. It will receive maintenance and security fixes until it becomes a legacy version.
The legacy version is even more stable than the beta. It is like a stable version but will only receive security fixes during the period of one year after its release. Some legacy versions (e.g. MediaWiki 1.19; see Debian/Ubuntu#Status), are designated as long-term supported (LTS).
Older versions are no longer supported and will not receive security fixes; see Version lifecycle.
Extensions can be classified as unstable, experimental, beta, stable, or unknown; see here for more details.