[alextp]

The historic picture makes a little more sense (though this is not something a 5yo would understand).

We call these things embeddings because you start with a very high dimensional space (image a space with one dimension per word type, where each word is a unit vector in the appropriate dimension) and then approximate distances between sentences / documents / n-grams in this space using a space with much smaller dimensionality. So we "embed" the high dimensional space in a manifold in the lower dimensional space.

It turns out though that these low dimensional representations satisfy all sorts of properties that we like which is why embeddings are so popular.