At some point yesterday, your flatmate or loved one probably ran headfirst into the room, iPad in tow, screaming about how YOU HAVE TO TELL ME WHAT COLOUR THIS DRESS IS, and then subsequently disowning you when you said blue/black. What the hell is going on? Here's an educated guess.
According to a few vision scientist friends (who were unwilling to put names to a theory due to threat of reprisals from the white/gold camp), the explanation probably has something to do with the two different types of cells that sense light in your eyes.
Your retina is comprised of rods and cones. Rods are more sensitive to light, but see shapes and not colour. Cones are sensitive to colour, but less sensitive to light -- i.e. in darker conditions, you're seeing more with rods than cones. You have three sizes of cones, blue (smallest) to red (biggest), as seen on the graph above.
Whether the dress appears as blue/black or white/gold depends on whether your eye has more rods or cones, and also the ambient lighting conditions in the room. (This is thanks to the different colours that are produced by additive and subtractive colour mixing.) Different people have different balances of rods and cones -- most notably colour-blind weirdos like myself -- hence different people seeing different colours, and families brutally murdering each other over this mess.
But rods are also very sensitive to light. Rod cells detect colour using a pigment called rhodopsin, which is very sensitive to low light, but is bleached and destroyed by higher light levels, and takes around 45 minutes to redevelop (why your eyes take time to adapt to night, in other words). Basically, if you look at the dress in bright light conditions, then go away for half an hour into a dark room and come back, the dress will quite probably change colour.
Moreso than anything else, though, this probably has to do with individual differences in colour perception. If you've ever dabbled with photography, you've probably come across white balance -- the camera trying to correct for the chromatic bias of the current lighting conditions. Your brain does its own white balancing automatically, meaning that you're either ignoring the blue hue, giving a white/gold image, or ignoring the yellow hue, giving a blue/black photo.
To wrap up the non-science side of things: according to Tumblr, the original dress is actually blue and black. But don't beat yourself up if you're seeing white and gold: a colour-picker investigation shows the colours, more or less, to be a pale blue and a muddy gold.