Your Tardis is having engine trouble - much like in the Doctor Who
episode "Journey to the Center of the Tardis
". The black box thing is the alien causing the trouble. Who knows if it's nice or mean, you fix the trouble in the end and are on your way. When the Doctor and Clara get to the center of the Tardis in that episode, the background is white with wreckage floating around - just like at the end of Antichamber.
You are the white cube...
...and the object of the game is to reunite with the black cube