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.
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.