The reason we can see the color of objects is light rays undergo scattering in the subsurface of a material, and in their walk in the material lose some wavelengths, and finally exit at a random direction (link)
However, aside from this, you see white highlights on an object from the light source. These can be diffuse or specular depending on surface roughness (I'm assuming they're both from surface interactions)
Look at the highlights on the shoulder here for what I mean. Not where the arrow is pointing.
However, I just found that that aside from metal, most common surfaces, even when highly polished, specularly reflect only a few percent of the incident radiation. How are these highlights then so pronounced, especially for the diffuse highlight case where the light is distributed in all directions.