A knowledge graph is a database of real-world entities — people, places, organizations, works — and the relationships between them, used by search engines and answer engines to disambiguate names and attach content to the right entity instead of a matching string.
Google introduced the term to a mainstream audience in the 2012 announcement "Introducing the Knowledge Graph: things, not strings", which framed entity understanding as the successor to keyword matching. Wikidata (open, community-maintained) serves a similar role in the open ecosystem and is a major source for other graphs.
For publishers, the graph is what lets a query about "Apple" surface the company versus the fruit, and what lets an answer engine attribute a quote to the correct organization when many companies share a name. The primary publisher-side control is sameAs — linking your on-site Organization or Person node to its Wikipedia, Wikidata, LinkedIn, and Crunchbase profiles pins your identity into the graph.
Answer engines lean on knowledge-graph resolution during both retrieval and generation. Retrieval uses the graph to expand the query; generation uses it to check attribution ("did this Person actually write for this Organization?").
The takeaway is boring but effective: fill in your Wikidata entry if you have one, and reference it plus your official profiles from every Organization and Person node you publish.