2700K = 4400F, but that's not what he means :)
The color temperature of a light source is similar to its overall color. In Fluorescent lights common color temperatures (abbreviated CCT for corrected color temp) are
2700 - reddish or warm
3000
3200
4100 - yellow but with terrible color rendition - only applies to fluorescent lights.
5000 - closest to sunlight at noon with a mostly clear sky.
6400 - bright white looks bluish if compared to 4100K and under but hardly at all if seen alone.
The numbers do come from temperatures in degrees Kelvin. If a piece of metal is heated to 3000 degrees K it glows the color of the light assigned the number 3000K. If you get it even hotter (and somehow it doesn't melt) to 5000 degrees K, it glows a more blue color. Lights that look that color are assigned a CCT of 5000K. It's very similar to a rainbow with lower temps red, slightly higher temps orange, then yellow, greenish, bluish. These are all shades of white, however.
These also correspond to peak wavelengths which is helpful if you're going to read some PAR charts/graphs and if you're interested in LEDs
Wavelength (nanometers) = 3,000,000 / Col temp (Kelvin)
So, for example, 3200K = 937.5 nm