From the mouth of the horse: "Wikidata is a free knowledge base that can be read and edited by humans and machines alike. It is for data what Wikimedia Commons is for media files: it centralizes access to and management of structured data, such as interwiki references and statistical information. Wikidata contains data in every language supported by the MediaWiki software." 
Wikidata interacts with MusicBrainz in various ways. This page is meant to note these various ways for MusicBrainz editors.
Interactions that affect MusicBrainz.
The most straight-forward are the Wikidata URL relationships. A few bots scour MusicBrainz and add Wikidata links to entities, but it can also be done manually.
Areas that exist in Wikidata will get imported into MusicBrainz by area_bot that runs every 3 hours, assuming a few conditions are set; namely that the Wikidata entry has the properties wikidata:Property:P31 ("is instance of") and wikidata:Property:P131 ("is in the administrative unit") set.
There are certain issues with area_bot that cause some valid areas to not get imported. Ping a Location Editor to have them import the area manually if area_bot fails to import it.
There are several properties in Wikidata for MBIDs, all of which can be used to link an item on Wikidata to MusicBrainz:
- Area MBID
- Artist MBID
- Instrument MBID
- Label MBID
- Place MBID
- Release Group MBID
- Series MBID
- Work MBID
The template Authority Control on the english Wikipedia will automatically include a link to MusicBrainz if the corresponding item on Wikidata has a claim with property P434. Because MusicBrainz also has MBIDs for people or groups who're not primarily involved in the music business, further restrictions apply: The MusicBrainz Artist ID is currently restricted to items that have p106 set to either
or are an instance of band. This list might not be complete, the complete one can be found in the template documentation or in the module itself. To whitelist further items and properties, a request can be made on the templates talk page.