I'm honestly a bit surprised that this whole thing is confusing and dividing so many people. This seems like a straightforward demonstration of Color Constancy (http://en.wikipedia.org/wiki/Color_constancy) and the distinction between local color and perceived color (http://practicalpainter.blogspot.nl/2010/05/local-versus-per...). I had thought that this kind of thing was more widely understood outside art education, but perhaps I'm wrong.
The short version is that the dress could be either and the photo doesn't really give enough context to say anything definitive. The longer version is that all color perception is relative. Light of a particular makeup of colors hits an object, it absorbs and reflects different amounts at different frequencies, and that's what hits your retina. Our brains then attempt to "reverse engineer" the "local color" of the object by comparing it to the surrounding light (presumably because local color is more useful for identifying and discriminating objects), and that's what we "perceive". In normal conditions we do this really well. But when you strip out the context, our brains keep trying but are easily fooled.
James Gurney tends to do an excellent job dissecting this phenomenon:
* http://gurneyjourney.blogspot.nl/2010/01/color-constancy.html
* http://gurneyjourney.blogspot.nl/2012/11/yellow.html
* http://www.amazon.com/Color-Light-Guide-Realist-Painter/dp/0740797719/