It's not a sponsorship, it's a sale.It's also made such deals with Yandex, Baidu, and Yahoo before. The sale is for eyeballs on your search (ad) service. Firefox is getting in a precarious situation with it though as the number of users on Firefox has been decreasing (in absolute terms) despite the number of web users increasing.
It's also a part of their anti-trust defense strategy. Firefox staying alive as a marginal but existent alternative to chromium based browsers is currently good for google.
