The game is played by one or more players, local or online, using their controller to hit a football, which is much larger than the cars themselves, into the opposing goal. Each goal gets one point, and whoever has the most points when the timer runs out wins. If both teams are tied when the timer runs out, it goes into sudden death over-time mode, where whoever gets a point first wins. The overtime game mode can theoretically last forever. There are also many various mini games and tournaments.
Source: Wikipedia, "Supersonic Acrobatic Rocket-Powered Battle-Cars", available under the CC-BY-SA License.