Looks to me like a white and gold dress that's being shaded from the ambient light. In reality, it's a black and blue dress with a yellow light cast on it.
Your mind naturally tries to compensate for color shifts caused by light. For example, a white car still looks white to you at sunset and in the moonlight even though it is actually reflecting that red or blue light, not white light (i.e. all colors of light). That's because your eye recognizes the general pallete of the ambient light and makes an interpretation automatically about the colors of the objects you see.
That's happening in this picture too, either correctly interpreting it as black and blue in yellow light or incorrectly as white and gold in shade. But even knowing it's incorrect, changing your brain's interpretation is not easy.
My guess is that some people don't see the gestalt, they get stuck on the actual RGB color values, which float around light gray/blue, and a dark gold.
From what I read at the time, there's an intrinsic lighting judgement being made. It could be one dress being lit in natural light, or another lit under a florescent bar. They both would produce the same RGB values.
Interestingly nobody has been able to replicate the effect in another image. It's truly remarkable and one of the best things off of the internet.
Because your brain doesn't just straight up show you the raw color value sent by your eyes, it tries to estimate the true color of the object based on lighting and context cues.
If you look at a chess board with a gradient shade on it, you brain will tell you the squares are black and white, even tough they are really all completely different shades of grey to your eyes. Depending on the context, literally the same color can appear black or white to you.
All because your brain is trying to be a smartass.
For the first time ever I saw white and gold with this instance of the picture. It scrolled from the bottom of my phone screen and I was wondering what this white and gold picture was.... Then I saw it was the dress and I recreated the effect for myself a couple times because I was shocked that I'd finally made the dress look white and gold!
Most of the time it's obviously black and blue, I wonder if this version is doctored slightly, because I've literally never seen it as white and gold before today.