The dress inside the [left] box is still black and blue (with yellow tint). Inside the [right] box the dress is white and gold, with a blue tint.

The black and yellow colors inside the boxes are actually the exact same color, and the same goes for the blue and white colors inside the boxes (which is what the seamless bars connecting them is there to demonstrate). But they look completely different, right? The picture is showing us two different ways the exact same colors can be interpreted differently depending on the context surrounding it.

The way this connects to the original image of the dress, is that some people see a gold and white dress because they think the dress is in blue-tinted lighting, as though they were standing in shade. People who see an overexposed image with a bright yellow tint, on the other hand, will likely see a blue and black dress. I couldn't tell you why it happens, but it's the way our brains perceive the lighting that's doing it.

If you go to my profile and look at my comment before this one, I posted two slightly edited versions of the image that better show how they're the exact same color.