Color temperature names a light by the temperature of an ideal glowing body that would have the same color. A hotter body shifts its output toward blue. For light that is not thermal, such as an LED, the figure is a correlated color temperature: the nearest match on that scale.
The scale describes real spectral differences, not just a tint. From Planck's law, a 3,200 K source, typical of a microscope halogen lamp, emits only about 0.29 times as much at 450 nm (blue) as at 650 nm (red). At 5,500 K the two are about equal, and at 6,500 K, a common daylight standard, blue is about 1.35 times red. A camera under halogen therefore collects roughly a quarter as much blue as red from blank glass.