Wikidata is a website, based on the Wikibase extension of the MediaWiki software, which aims to be a centralized, human- and machine-readable database, analogous to how Wikipedia is a centralized encyclopedia. Wikidata 
One important function of Wikidata is that it is "glue" for the various language editions of Wikipedia, as well as Wikimedia sites such as Wikimedia Commons, Wikivoyage, and Wikisource. It provides connections between, for instance, the Wikipedia articles about New York City in English, German, and Chinese, as well as photos and videos from New York City on Wikimedia Commons, and travel guides on various language editions of Wikivoyage. It also offers data (such as demographics, geographic coordinates, etc.) which may be accessed by those sites, for instance for their infoboxes.
But Wikidata is also available for database queries of all kinds through a public query language, SPARQL Query. With this language, it is possible to easily get, for instance, a list of all female painters (who have an entry in Wikidata) with parents who were scientists, or a map of all newspapers (with an entry in Wikidata) in Washington State that have a Wikipedia article.
There are a number of websites and videos that offer an introduction to SPARQL Query. This 40 minute video is a good introduction: Building SPARQL queries - Wikidata tutorial by Navino Evans
Queries may be built and executed at the site Wikidata Query Service . The "examples" button on that page is an excellent way to explore the possibilities. Be sure to click the blue "Play" button in the lower left to execute each example.