What does a chameleon's skin do to change colors?

Aside from camouflage, changing skin colour helps chameleons to keep their body temperature in a suitable range. These animals are unable to generate their own body heat.

chameleons change colors by rearranging a lattice of nanocrystals in one of the top layers of skin cells

https://www.science.org/content/article/secret-chameleon-color-change-tiny-crystals

These cells are called iridophores, which have crystals made from guanine. Normally, their highly ordered arrangement means they strongly reflect a particular light colour. But by stretching its skin cells, the crystalline lattice changes shape, so reflecting a different wavelength of light.