An embedding is the output of a model: a sentence turns into a vector of a few hundred or a few thousand numbers. The trick is not in the numbers but in the fact that vectors of sentences with similar meanings land close to each other — so the machine finds the paragraph you were after even when you asked for it in completely different words.
This is the foundation of every meaning-based search and of RAG. And it is far cheaper than most people expect: ten thousand vectors come to roughly 75 megabytes — that fits on a phone. The question is not whether you have the space, it is whether the chunking underneath the embeddings is any good.
The most common misconception is that an embedding understands the text. It does not — it measures statistical similarity. That is why it falls over wherever the exact word matters: a part number, a legal reference, a rare proper noun. Keyword search does better on those, and the two together do better still.
The mechanism and the four typical traps are laid out in Embeddings and Vector Search, Explained Clearly, one trap at a time. Directly related terms: vector database, chunking and hybrid search.