Static analysis of lots of human translators' output. Given the input and output of a strange human filter, they're trying to approximate the filter using machine learning. When their algorithm's output approximates the best translations, they're done.
That's one way to train a translation system, but that's not related to the Translate API -- I'm asking, what benefit does Google receive from usage of the API? They already have the entire Internet in their index -- it's not like they need a better source of what phrases exist. The parent implied that Google was using the API to train their MT systems, which I find hard to believe.
GOOG-411 is an example of this process. Google got voice samples and users got a service. When the voice training parameters stopped getting better the service was shut off.