It's like recaptcha, you should look at Luis' TED talk: http://www.youtube.com/watch?v=cQl6jUjFjp4

Apparently, They sell translation services.

We the students make the money for them helping to translate the web into other languages we are learning.

In the immersion category, people pay for their documents to be translated. We translate them for education purposes, and Duolingo makes profit once the document is fully translated.