This diagram shows the variations in color a black body goes through as the temperature increases right?



How or why does this relate to natural light white balance?



Is it because the Sun is a black body and is also our source of natural white light?

There is simply no way of accurately representing a blackbody radiation in a simple blue/amber representation...it would behoove you to ignore the graphic represent and try to understand the theory. OK?

Jeff is correct in that the graphic is an oversimplification, but it has proven useful in practice. A very similar graphic is shown in this link (scroll down about a third way) and is cited as coming from Kodak and MIT and is thus authoritative. A similar representation is shown here along with the spectral power distribution (SPD) of the sun as seen from above the earth's atmosphere. The sun is not a perfect black body radiator and the SPD of sunlight is further modified by water vapor and pollutants in the atmosphere. On the other hand, a tungsten lamp closely approximates a black body radiator.

The color temperatures shown in the graphic are correlated color temperatures. See the first link or Wikipedia for further explanation.

And there’s this:
http://www.ppmag.com/reviews/200512_rodneycm.pdf
http://www.ppmag.com/reviews/200604_rodneycm.pdf
http://www.ppmag.com/reviews/200605_rodneycm.pdf

It is important to note that you can have two real lights that have the same correlated color temperature (CCT) (e.g., 5000 K) but very different appearance. A real scene illuminated by these two different light sources can look significantly different. The plots are useful but limited. It would be like trying to understand geography purely in terms of time zones. Saying that somebody lives in the Eastern Standard Time zone does not really tell you whether that person is in New York vs Florida, for example. It only tells you that somebody living in EST is likely somewhere east of somebody living in PST ...

Eric brings up an important limitation of the CCT plots. The more the spectrum of the source differs from that of a black body radiator, the more likely one will see color matching problems. Sources with discontinuities in their spectra (such as some florescent lamps) can cause problems. The CRI (color rendering index) attempts to quantify these mismatches. Virtually by definition, tungsten bulbs have a CRI close to 100, but are not ideal for digital photography because they are deficient in blue. A Solux bulb is near ideal and florescent lamps with special phosphors (full spectrum) can also produce good results.

Yes, Bill, tungsten bulbs can be very good in the color department but due to the low blue energy there will be issues of noise.

Eric, I would think that the Solux with at 4700K would be pretty good for most digital cameras. Or with a regular 3200K one could use an 80a to convert to daylight. However, that might not be optimum, since no digital camera has a native white balance of daylight AFAIK. Do you have information on the optimum filtration for various digital cameras?