You'll help them get through each room by physically interacting with them, or other objects in the room, by using the front and back touch pads, etc. Some basic examples:
* You swipe across the characters to start them moving across the screen, then tap them to stop.
* You might flick an object out of the way, tap it from behind to move it towards you, or flick the blades on a fan to get them spinning
* You can "pinch" the characters (squeeze the front and back of your Vita at the same time) to make them sprint, or to squeeze the gas out of one character.
Some puzzles have timing elements, and some you just need to use the right combo of subtle moves. Some are very straightforward, and some are horrendously devious.
The game looks terrific -- it's a monochrome world, but there's a ton of character in every fine details of the game. Everything is fluidly animated, looks and acts "real", even though it's a surreal universe within the game.
Sounds are minimal, soundtrack is well-suited if not super memorable.
The game is best played in short sittings -- you'll get tired of it quickly if you try to play through the levels in large chunks. When I play it 3 or 4 levels a day, it all feels fresh and fun.
In short, if you like physical puzzle games (Limbo, Braid), then this might be a good one for you. If you're looking for more of an action platformer (Rayman), this may not be ideal.