The Leather Ball is an oblong ball made comprised of a patchwork of leather stitched together. This ball can be thrown to the ground for a dragon to chase and return to its trainer: effectively producing a game of fetch that the trainer is able to play with their dragon.
At some point before the events of School of Dragons, the Leather Ball was created by Hiccup in order to help trainers play and bond with their dragons.
During the events of the game, Hiccup gave the ball to the player once they had obtained their first partner dragon so that they could play with their dragon and create a closer bond with it. The player can use the ball whenever they wish to up the happiness of their dragon and forge a stronger bond together.