The game opens with an amnesiac Kat waking up in Hekseville, a floating city around a structure called the World Pillar. Kat is accompanied by a mysterious cat named Dusty; in saving a boy from being swept up in a gravity storm, she discovers that Dusty has the ability to manipulate how gravity affects her, enabling her to help people fight monsters spawned from the storms called Nevi. After saving Syd, a police officer who becomes her friend, she learns that those with her powers are dubbed "Shifters" by Hekseville's people. As she begins helping the city's denizens, she is confronted by fellow Shifter Raven, who sees her as an enemy.
Kat navigates the game's open world of Hekseville both on foot using roads and walkways, and using her powers; activating Kat's abilities, the player tilts the PlayStation Vita, aiming Kat and allowing her to "fall" in that direction. Kat can use her abilities to walk on vertical surfaces or areas such as ceilings and the underside of structures. Kat's gravity-based abilities are tied to an energy meter which decreases when her powers are active. When fully depleted, Kat's powers deactivate until the meter recharges.
Source: Wikipedia, "Gravity Rush," available under the CC-BY-SA License.