Comment Purkinje Effect (Score 1) 420
There are several factors that make this unintentional optical illusion really interesting.
The first, demonstrated by the xkcd, shows that the colours will appear markedly different with different coloured backgrounds. It doesn't fully explain what we are seeing here though, as people are seeing the two different states with the same background to the dress.
I believe that the main illusion comes down to the Purkinje Effect, and how our brains interpret colour. Under the Purkinje Effect, in lower light levels our peak visual sensitivity shifts to the blue end of the spectrum. At higher levels it shifts away from the blue end of the spectrum as the rod cells in our eyes reach a point of saturation and stop being effective. So, when ambient light is bright enough, we just don't perceive blues as well, and we just don't see differences in contrast as well (as the rod cells are responsible for contrast vision).
If your eyes are adapted to bright light conditions (and the threshold here varys from person to person), you will likely see white and gold. Due to the shift away from blue, dark greys in the image appear more yellow. The blue also becomes apparently lighter to the point that our brains interpret it as a white dress in the shadow in daylight. If you go into a darker environment and wait (it takes about 10-15 minutes for the rhodopsin in the rod cells to regenerate), you willl likely see the blue and dark grey/black.
The first time I saw this, I had just walked in from outside. I saw white and gold. Then after sitting in a darkened workshop for 30 minutes, I saw it as blue and dark grey.