Now that everyone is bored with arguing over the color of a dress, along comes a photograph of a cat with the question of whether it is walking upstairs or downstairs. However, this is basically an appropriation of an optical illusion listed in Wikipedia as the Schroeder stairs. Here is the original version:
The basic idea is that you can view either A or B as the outer face of a stair structure. The the first case you see stairs descending to the floor; in the second case they are rising to the ceiling. As the Wikipedia author observed, this illusion inspired Escher's "Convex and Concave."
In this case a photographer figured out how to photograph a staircase to allow for the same kind of ambiguity in interpretation. The cat was then added just to make the image interesting. The point has less to do with the reality of the setting in which the photograph was taken and more with how it reproduces a classical optical illusion, older than the cat and everyone looking at the photograph.