To use Andrew Ng's example, you have build a multi-dimensional arrow representing "king". You compare it to the arrow for "queen" and you see that it's almost identical, except it points in the opposite direction in the gender dimension. Compare it to "man" and you see that "king" and "man" have some things in common, but "man" is a broader term.
That's getting really close to understanding as far as I'm concerned; especially if you have a large number of such arrows. It's statistical in a literal sense, but it's more like the computer used statistics to work out the meaning of each word by a process of elimination and now actually understands it.