The light that is illuminating an object. The perceived color of an object (the light that reflects off of an object) is the product of the object’s reflectance (its inherent color) and the color of the illuminant. When the illuminant is white, the perceived color is equal to the object color. When the illuminant is not white, the perceived color is “distorted”.
The illuminant tends to be a color on the Planckian Locus, one of which is D65, a definition of white that represents average daylight. Other colors on the locus are described as “warm” or “cool”, but are mostly considered white.
While the illuminant can determine the perceived color, the observer’s visual system can usually estimate the object’s color through a process called Color Constancy where the illuminant’s color is “subtracted” from the image. The disagreement behind The Dress was due to different people interpreting the illuminant as being “warm” or “cool”, and subtracting that color accordingly.