Take the word "king." Your database does not store the word. It stores a vector: a list of 768 numbers that place king at a point in space, where words used in similar ways sit nearby.
That one move changes the whole problem. "Find something similar" becomes "find the nearest point." And finding the nearest point in a space of hundreds of dimensions turns out to be the search your normal database index genuinely cannot do.
Meaning becomes a place
An embedding model reads enormous amounts of text and learns to place each word (or sentence, or image) at a point, so that things used in similar contexts land near each other. Closeness is usually measured with cosine similarity: how aligned two vectors are, ignoring their length.
from sentence_transformers import SentenceTransformer, util
