The hover crafts are used by the Capitol for many things. They use it to transport the tributes to the arena for the Hunger Games. During the Hunger Games they take the dead tributes from the arena once everyone has left the area. They are also used to capture people who have escaped from their district in the woods. After the Hunger Games concludes it take the winner to the capitol and while on board they are given medical care. The rebels use them to break Katniss and her allies out of the arena at the end of Catching Fire. Once the force field is down they drive it in, pick up the tributes they need for the rebellion and the leave. They are headed to District 13 which was thought to be destroyed but is actually the headquarters for the rebellion.