A word lives in a space of hundreds of directions. You cannot picture that, and you do not need to, because you already work in many directions at once whenever you describe a person.

Take five sliders: how tall they are, how old, how loud, how kind, how funny. Each person is one setting on each slider, which is a point in a five-direction space. Two people whose sliders read alike are similar people. No picture required. You just read the settings.

An embedding is the same arrangement with more sliders. One difference: these are not labelled. Nobody set aside a slider for animal or friendly. The numbers arrive as a pattern, learned from use, and it is the pattern as a whole that places the word.

So: an embedding is a long list of numbers, and lists that read alike tend to mark words used alike.