"Color Temperature" is a way of measuring or describing the relative intensity of the individual colors (wavelengths) that make up visible light - that is, its spectrum.
A simple way to grasp the general concept is to picture a standard, clear, incandescent light bulb on a dimmer. With no current flowing, the filament is cold, and there is no light emitted. Turn it up a bit, and the filament gets hot and starts to glow red. At that point, its emitted spectrum is primarily on the red end, with little of the other wavelengths. Turn it up more and more, and it gets hotter and hotter, the intensity of the other wavelengths starts to increase, changing the color from red to orange to yellow, and eventually to bright white.
It is important not to confuse color temperature with intensity. The color temperature, expressed in degrees Kelvin, is only an expression of the relative intensities of the various wavelengths that make up light. In fluorescent light bulbs, where the phosphor and not a filament determines the spectrum, it is possible, for example, to have a 25 Watt bulb and 100 Watt bulb with the same color temperature, but obviously there is a lot more absolute light intensity from the 100 W bulb.
Also keep in mind that these are spectra emitted from a "black body", and while it does apply directly to light sources like the sun and artificial lights having glowing filaments and electric discharge lamps like MH and HPS, it does not directly apply to fluorescent bulbs and LEDs. The numbers expressed on those are corrected color temperatures - "corrected" to fool the human eye into thinking it is the same as the black body.
So what effect does any of this have on us? The human eye and brain adjust and compensate very well, so many light sources look "white" to us. Under some lighting extremes however, flower colors may look a little "off". Unfortunately, camera film and digital sensors do not adjust well, at all. That is why an image captured under fluorescent lighting may look "cold and blue", while those under incandescent light may take on a yellowish hue. Similarly, plants do not have the capability of making such an adjustment, so it is important that we provide them with the proper spectrum of light - especially when employing artificial light sources.
We know that the chlorophyll in plants need light that is primarily in two color ranges - the 400-450 nm (nanometer - one billionth of a meter) "blue" end of the visible spectrum, and a slightly lower intensity in the 640-680 nm "red" end. In summer sunlight on a clear day, when the incoming light is a combination of direct rays plus atmospheric reflections, the spectrum most closely matches the absorption spectrum of chlorophyll. With both natural and artificial light sources, the "balance" between those ranges varies greatly. Click on a light source below to see an approximation of the spectrum.