The idea is that you play as Kat, a girl wandering around a dreamlike, stylistic city called Hexaville (complete with a pink sky and a comic panel look) who finds herself with the ability to control her own personal gravity, floating up in the air with a flick of the R trigger. Once floating, you can use the right analog stick (or, more likely, the PS Vita's gyroscope) to aim her towards a wall or building, and then the R trigger sends her flying across the world that way, changing up gravity until you hit the R button again and bring her back down to the ground.
It's as trippy as it sounds, and when you learn (from a mysterious yet helpful magical black cat) that hitting the R trigger anytime in mid-flight will send you into a floaty state, you figure out that Kat can basically fling herself around the world at will, pausing in mid-air, twisting the Vita around in real space to re-aim her at some distant target, and then firing her ragdoll body off again.
Later on in the demo, the gameplay starts to include combat. Kat is attacked by some red and black blob enemies, and you've got to fling her at them by floating up and landing with a well-placed kick. But the game's very forgiving, especially in these early stages. The combat is really just there to keep things interesting -- the real core gameplay seems to be just making use of the Vita's controls to move Kat around the world. The Sony rep showing off the game said that Kat would pick up more abilities as the game went on, however, and that other Vita features (like the touchscreens and possibly even the dual cameras) would be used as well.
There is of course a story surrounding Kat, and it's told with comic book-paneled cutscenes between the levels, which you can flip through with a touchscreen swipe. You can also use the gyroscope to tilt the view for a sort of pseudo 3D, but that's more of a gimmick than anything; it does make the "page" a little more tactile, but it doesn't affect gameplay.
All in all, Gravity is an interesting title -- it likely won't grab as much press as the bigger headliners in the PS Vita's "launch window" lineup, but it seems like a well-made and original way to show off just what that gyroscope in the Vita can do.