A vector database stores information as embeddings (long lists of numbers that capture meaning), and finds results by mathematical similarity rather than exact keyword match. Ask it for things "like" a query and it returns the closest vectors, which is what makes semantic search and retrieval-augmented generation possible.
It is a specialised tool, not a replacement for your primary database. In most systems it sits alongside a normal relational store: the relational database holds the source of truth, and the vector index makes it searchable by meaning. Choosing one, sizing it, and keeping it in sync with the source data are the practical decisions.