Of course there are already a ton of broadband tests available online, so the FCC is not just looking to provide another free service. Instead the government agency will collect your location information (like other tests do to a certain extent, anyway), using anonymous aggregate data to "analyze broadband quality and availability on geographic basis" and form its national broadband strategy.
The FCC is working with two independent companies to test broadband speeds: Ookla and M-Lab. Users are randomly assigned a testing application from either company. Those without broadband can alternatively fill out a small survey asking if there is no availability in their area, and if they would be willing to subscribe to broadband if it were available.