Learn how semiconductors can produce light. The key is that the material composition determines how much energy will get put into the electrons, which determines how much energy they put out as light.
Understand that indium gallium nitride (InGaN) can be fabricated so that it puts out a lot of blue light, but that it's a difficult material to construct. That's why Cree builds their diodes on a SiC substrate: to give a solid base to build the InGaN crystal.
Notice that LEDs give light of just one color, determined by the structure of the semiconductor. Cree's InGaN can make several colors, but blue comes in particularly handy.
Learn about wavelength conversion. This is what happens when a phosphor absorbs light of a short wavelength and emits light of a longer wavelength. For Cree, the short blue wavelength gets absorbed by a phosphor that emits yellow and/or red light. The light from the phosphor combines with blue light that makes it through from the diode, creating white light.
Understand that Cree lights are usually created from many LEDs operated together, creating a rich blend of light.