image behind spoiler tag:
Basically, what is going on is that our brains are making things up. If you turn back to your basic grade school biology, you will recall that the color of an object is actually the result of that object reflecting back the light frequency of that color, while absorbing the rest of the light frequencies. But there is more to it than that. You also have to filter out the spectrum of the illuminant objects such as light bulbs or the sun. This allows you to make figure/background distinctions and not just get lost in the wash of light. Your brain is doing some computation here to give you a sensible experience, so it's also taking the surrounding context of the object into account. For a more clear example, view this optical illusion:
In the case of the dress, a big part of the distinction is also in how accustomed people are to adapting for natural light or electrical light. Those that are more used to adapting to electrical light are more likely to see the black & blue image, or so I've read.
But our friend who is the visual perception expert challenged us to think about the meaning of this finding a little bit deeper. Our perception of reality is not reality. It's an approximation. An experience that is both empowered by our biology, but also limited by our biology. We don't have a pure way of understanding everything about light, and color is kind of a thing our brains made up to make sense of it, but they are fallible and can be wrong- even though you feel with certainty that you are seeing blue & black... or white & gold. As Alfred Korzybski famously said "The map is not the territory", or the Buddha before him "My finger pointing towards the moon is not the moon" (which was the Buddha's way of explaining that his teachings were not enlightenment, but simply instructions about a way towards enlightenment).
Similarly, we don't perceive the world the same way that other animals do. Bats can use echolocation to hear with such fine grained fidelity that it gives them a similar amount of information about their environment that sight gives us humans. Dolphins use sonar. Many fish have electroception, that allows them to perceive electromagnetic fields to perceive other things in the ocean. Humans have no way of truly understanding the experience of these animals because they lack the needed perceptual abilities. I bring up the classic Matrix line that "there is no spoon" because really, our brain's thoughts and perceptions are just cognitive maps of reality that don't fully represent the entirety of the territory. They are inaccurate projections. We only understand reality through our perception, but there is so much more there that we cannot perceive, and even some things we do perceive that actually are not there.
There are actually lots of cool optical illusions (and other perceptual illusions) out there, and I recommend looking them up and learning about the boundaries of your perceptual systems' accuracy. One of my favorites is the spinning dancer. You will likely see her spinning clockwise, but if you look at her in a certain way you can also see her as spinning counter-clockwise. It helps if you first tell yourself that her planted leg is either her right or left leg and then force yourself to believe that, then you can mentally reverse the spin.
And one final take on the Blue & Black vs White & Gold optical illusion:





