Colour temperature or Correlated Colour Temperature (CCT) describes the colour appearance of white lights sources, when compared to an ideal black-body radiator heated to the corresponding absolute temperature in degrees Kelvin (K).
Therefore as a black-body radiator is heated the colour appearence of the emitted light will change from a warm red-white glow at low temperatures to a bright blue-white at high temperatures. The curved line through the centre of the CIE diagram below is refered to as the black body locus, the isotemperature lines crossing the black body locus define the correlated colour temperatures, therefore unless the colour temperature of the measured light source falls directly on the black body locus, it should be considered as a Correlated Colour Temperature (CCT).
The measure is therefore used to describe the appearance of artificial light sources in comparison to the black body through plotting the X Y Chromaticity co-ordinates on the CIE diagram, as shown below. If we consider the extend of the isotemperature lines crossing the black body locus, we can see that a light source with the same measure CCT could actually have slightly different spectral composition and therefore colour appearance.
This is the reason why all light source with a 3000K or 4000K CCT are not exactly the same. Ideally you want to be selecting a light source with chromaticity co-ordinates as close as possible to the black body locus for the best and most accurate colour appearance, when compared to a black body radiator.
MONO LEDs are carefully selected from bins as close as possible to the black body locus for each selected colour temperature.