It is commonly found throughout the game, and is first introduced in Grab and Swing by Larry Da Vinci. The powerup can be used by both Sackboy and any programmed sackbots, and is found in the "Character Enhancment" bar in the tools section. The lighted bits on the Grappling Hook change color with the player's Popit.
The Grappling Hook, as it's named suggests, is used to grapple on grabbable hard-to-reach areas. It can also be used to pull two-way and three-way switches. The player can then swing from the object to get to higher, farther, or more difficult areas of play. It's length can also be reduced or increased to a certain degree. The Grappling Hook can also be used to pull other characters or objects towards the player. If you stand too far away from a grabbable object with the hook, you will hear a buzzer-ish sound.
In LittleBigPlanet Karting, the grappling hook is avaliable and does the same basic function as the one in LittleBigPlanet 2', which is to help leap over big openings in the ground.