The pneumatic is a very fast form of transportation which the elves use to travel around the North Pole.
In the film, while lost in the North Pole, Hero Boy, Hero Girl and Billy arrive at the Communications Room where they see a few elves doing some last minute work. After they finish, they take the pneumatic to get to the North Pole with one of the elves noting that it is the only way to get to the square on time. The children decide to take the pneumatic too, but they end up in a toy factory instead.
One of the levels in the video game requires the player to operate the pneumatic and make sure it hits the right colored gate.