A broomstick was a device ridden by a single rider in order to fly within a planetary atmosphere.
Harry Potter was a broomstick-flying ace, even possessing a broomstick that could reach 240 km/h from a full stop in ten seconds. ("Harry Potter and the Return of James T. Kirk")
In an alternate universe encountered by the Stoneship in 2402, broomsticks were common on Taladu and ridden by magic practitioners. (Star Trek: The Stoneship Files: "Alcoholic Massacre, Part I and Part II")