What is an embedding, in plain terms, and why does 'closeness' between embeddings matter?

An embedding is a list of numbers (a vector) that represents a piece of text's meaning in a high-dimensional space, produced by a specialized embedding model. Texts with similar meaning end up as vectors that are close together (by cosine similarity or distance), which is exactly what lets a vector database find 'similar' documents to a query without any exact keyword match.