There is no such thing as "white" light. Your brain looks at the color of everything around, takes an average, and decides that that is white. So sunlight (color temp about 6500 K) looks white during daytime when everything is sunlit. But if you use a 6500 K light bulb at night, it looks blue because most artificial lights are around 2500-3500 K (orange-red). Most of the things your brain is seeing are lit by orange-red light, so your brain decides that orange-red light is white. Then when it sees the 6500 K light, it sees that as blue.
A color profile (ICM profile) is different. The monitor's representation of different brightness colors does not fall on a line (I'm simplifying - the actual brightness scale is logarithmic.) A...