FEZ is a game where you control a cute little white-blob creature called Gomez. Gomez lives in a 2-D world where no one believes in cubes, which they call "devil squares." Why and how they have a superstitious name for cubes, when, as two-dimensional creatures, they have no frame of reference for such things, is not explained.
Anyway, the common beliefs are wrong. Cubes do exist, and are, in fact, essential to the functioning of the world. When the big cube breaks, the leader of the community, Geezer (who looks suspiciously like a future version of Gomez), tasks Gomez with saving the world, and gives him a magic Fez that lets him travel through the mysterious third dimension by rotating the world. Using this ability, he can overcome obstacles that are ordinarily impassible and find secrets that are hidden in the incomprehensible corners of the world.
The goal of the game is to collect cube shards, to assemble into cubes, to open doors, to find more cube shards. You know, typical platformer stuff. Overall, I really like the game. Navigating the levels, flaunting the rules of space by rotating the map, and figuring out tricky jumps are a blast. My one complaint, thus far, is that backtracking is a pain in the ass, so if you miss something in a level, replaying the level to do extra exploring is not especially viable. I think this is caused by things like one-way portals, non-obvious connections between levels, and jumps that are easier to make forward than backwards. Plus, the world map is basically useless.
It's not enough to discourage me from playing the game, but I anticipate that if I ever get to a point where my forward progress is stymied, I mind find the structure of the game to be incredibly frustrating.
Though, it's probably a bit premature to be so pessimistic. Thus far, the game is a brain-bending delight.