Its main purpose is to propel the player in any way they desire. The gear is especially useful when reaching hard-to-reach places (Iron Mine-Chan, The Masked Man) and because of this, it is one of the most sought-after gears in the game.
The gear made its debut in The Outdoors Update. As the maps were constantly changing, so did the location of the Jetpack, from a tree, to an obby under the map, to on a hidden island and the Ice Plateau.
The Jetpack is stocked on a tree branch located near the center mountain. Note that there is an invisible barrier that is blocking you from reaching the Jetpack by standing on it. You would have to jump off and have a limb touch any part of the Jetpack's sides that happen to be unblocked by the barrier.