A vector database searches by meaning instead of matching keywords. First, an embedding model reads each document and turns it into a long list of numbers. Those numbers are coordinates: every document becomes a point in a high-dimensional space, and documents with similar meaning land close together.
When you ask a question, it gets embedded the same way and lands in that same space, right next to the documents that talk about the same thing. Answering your query is now geometry: find the nearest neighbors. That trick powers semantic search, recommendations, and the retrieval step in AI assistants (RAG).