Embedding
A short list of numbers standing in for something complicated, arranged so that similar things end up close together.
Contrast it with one-hot encoding, where every pair of categories sits at exactly the same distance — the representation contains no information about similarity at all. An embedding's geometry carries meaning, so distance between two vectors is a usable answer to "how alike are these".
Typically 128 to 3072 dimensions of floats. L2-normalise them and a dot product becomes cosine similarity, which is what almost every vector index assumes — skip the normalisation and long documents win your rankings regardless of relevance.
The operational rule that catches everyone: an embedding is only comparable to vectors from the exact same model. Change the encoder, or its version, and every stored vector has to be recomputed, because the two spaces are unrelated. Mixing them produces no error, just quietly meaningless neighbours.