At the core of statistical machine translation, and other things (Google)

NYTimes Magazine, Gideon Lewis-Kraus, The Great A.I. Awakening:

When you summarize images, you can divine a picture of what each stage of the summary looks like — an edge, a circle, etc. When you summarize language in a similar way, you essentially produce multidimensional maps of the distances, based on common usage, between one word and every single other word in the language. The machine is not “analyzing” the data the way that we might, with linguistic rules that identify some of them as nouns and others as verbs. Instead, it is shifting and twisting and warping the words around in the map. In two dimensions, you cannot make this map useful. You want, for example, “cat” to be in the rough vicinity of “dog,” but you also want “cat” to be near “tail” and near “supercilious” and near “meme,” because you want to try to capture all of the different relationships — both strong and weak — that the word “cat” has to other words. It can be related to all these other words simultaneously only if it is related to each of them in a different dimension. You can’t easily make a 160,000-dimensional map, but it turns out you can represent a language pretty well in a mere thousand or so dimensions — in other words, a universe in which each word is designated by a list of a thousand numbers. Le gave me a good-natured hard time for my continual requests for a mental picture of these maps. “Gideon,” he would say, with the blunt regular demurral of Bartleby, “I do not generally like trying to visualize thousand-dimensional vectors in three-dimensional space.”

Still, certain dimensions in the space, it turned out, did seem to represent legible human categories, like gender or relative size. If you took the thousand numbers that meant “king” and literally just subtracted the thousand numbers that meant “queen,” you got the same numerical result as if you subtracted the numbers for “woman” from the numbers for “man.” And if you took the entire space of the English language and the entire space of French, you could, at least in theory, train a network to learn how to take a sentence in one space and propose an equivalent in the other. You just had to give it millions and millions of English sentences as inputs on one side and their desired French outputs on the other, and over time it would recognize the relevant patterns in words the way that an image classifier recognized the relevant patterns in pixels. You could then give it a sentence in English and ask it to predict the best French analogue.

There's much more to the article, which is well worth reading. But those two paragraphs seem to be the conceptual heart. The rest if a matter of figuring out how to turn that conception into a practical system.