O.K., time to throw some facts into this thread...
Color temperature is a way of describing the color of a light by comparing it to a glowing hot piece of platinum metal. Heat the metal and it begins to glow, first red then more yellow, and eventually even blue.
Note that there is white on the scale above, but that's just because of how I drew it. There technically is
no white on a color temperature scale. I say
technically because there is a shade of yellow at around 5500ºK that our eyes tend to interpret as white since we evolved in sunlight of this color. But it is actually yellow.
And comparison to the colors in the rainbow are not really appropriate either - there is no green on a color temp scale.
Color temperature is always measured in degrees Kelvin (or, more accurately,
Kelvins, without the word "degrees"). The Kelvin scale is the temperature scale normally used in physical sciences like astronomy. It is like the more familiar Fahrenheit or Celsius scales, except 0º on the Kelvin scale is Absolute Zero - the temperature at which there is no heat energy left in an object.
So what color temperature do we want lighting our reef tanks? Well, the sun overhead at noon is yellow-white at about the 5500°K to 6500°K range. But "daylight" as we see it is a little more blue than that because of reflected light from the blue
sky. Furthermore, red and yellow light do not penetrate water very well, making light underwater more blue.
So the easiest answer is "Somewhat more blue than 5500°K."
Color temperature is
not a simple case of "higher is better" - lighting your tank with light that is too high in color temperature deprives the corals of energy in many of the color ranges needed for photosynthesis (photosynthesis in reality is not this simple - there are a wide range of photosynthetic symbiants in coral and each one has a different mix of photosynthetic pigments, each of which responds to a different color range.)
So, all that being said, there are two important "gotchas" -
1) Color temperature represents a continuous spectrum of colors. Any given color temp, be it 4000ºK or 10,000ºK is a mix of all the colors in the rainbow (yes, even green), but with a characteristic curve peaking at a certain wavelength. Color temp is a valid measure of the color of any continuous specturm source like an incandescent light. Makes sense if you think about it - color temp is the temperature you heat a glowing piece of metal to, and an incandescent bulb works by means of a glowing metal filament. Color temperature
does not accurately describe the color of an emmision spectrum. Emmision spectra result from photons emmited by the electons in an excited gas. All of the light energy is concentrated into a few discrete wavelengths instead of being a mix of all colors. Examples of lighting that produce emmision spectra include: You guessed it -
Metal Halide and Fluorescent! So when you see the color temperature specified for one of these bulbs
it means absolutely nothing. It's just the marketing manager's opinion of what will make the bulb sell. This is why we can have 8 different 10,000ºK bulbs in this hobby, all with different colors - none of them are actually 10,000ºK, or any other color temp for that matter.
2) In general, the higher the color temp rating, the lower the intensity. So in many cases a yellower bulb will be better for your corals due solely to the increased intensity.