Based on the references above, I get the sense that it allows a being to change their color and to an extent, their texture, or at the very least the surface texture of their body. Being the same color as a tree won’t hide you very well if your armor is still glossy and reflective.
In terms of real life parallels that we can draw information from, Chameleon is unfortunately not the ideal name for the power; chameleons in general don’t actually change color to reflect their surroundings. Their colors change based both on mood and their temperature. Dark colors absorb more heat, so a cold chameleon may darker it’s skin in order to absorb warmth more efficiently.
Octopuses however, have access to both the chromatophores in their skin to change color and the ability to vary their texture. I’m not certain to exactly what extent, but by scrunching up, their surface becomes bumpier and more closely resembles moss or seaweed, while flattening out/stretching their surface gives them a smoother taut appearance. I could see beings with the Chameleon power doing something to their surface similar to manipulating ferrofluid, where they can control both the color of the material, and whether or not their skin/armor is smooth, pointed, bumpy, or any combination therein depending on their surroundings.