Color temperature of a light characterizes the energy distribution of its radiation within the spectral emission of the light source. It's reckoned in degree Kelvin. Low values (from 2000 to 3500 K) correspond to warm tones (yellow-orange light) whereas high values (from 4000 to 6000K) correspond to cool tones (white-blue light).
Color temperature changes the perception of the space and the enlightened objects and thus becomes a factor of style. A tone of different light will be used according to the colors of objects, or according to the atmosphere wanted in the various places. A warm light will tend to be less bright visually and to make colors more mat, but will give a warm side to the space / to the object. Whereas a cool light, visually more bright, will make shine the colors of the space and the objects, but will give them a colder and more raw side.
The neutral color, 4000K can be considered as a white neutral light.
The LED technology manages today to reproduce quite various temperature of lights and so allows to illuminate spaces in a optimal way. (See the article on the advantages of the LED)