The Alien Ruins Dimension is the final area of Fez. You access the area by collecting a total of 32 cubes and entering the door in the New Village that requires that amount. Going through it will take you to a Star Gate, as said by Dot. It will activated a few seconds after you enter the room and become a portal to the dimension.
Once you enter the dimension, you are no longer on the map of the game world. The main gig of this dimension is that you can jump high, fall slowly, and can fall longer distances without taking fall damage.
The only thing you can do is climb to the top of the ruins that are around you by scaling some tricky platforming. Once you are at the top, you will see an Owl Statue and a doorway made of light that is rotating on its own to different perspectives. Go though it with accurate timing and you will get either the 32-cube ending or the 64-cube ending, depending on how many cubes you have.
The Alien Ruins Dimension is the only place in the game without any collectables in it, which is perhaps because its a different dimension than where Nine Circles exploded in the beginning of the game. Also, unless you know how to make good use of the internet, you'll likely have to go through this area multiple times in order to get the required First-Person Shades (from the 32-cube ending) and the 64-cube ending.
A similar room can be seen in the sky ruins where you can meet an Owl who says :
"A point of origin. Above and beyond."
which refers to the track of the Alien Ruins Dimension called Beyond.