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We see an object because light is reflected from its surface into our eyes. That is, ALL all light is reflected light. This may sound confusing at first because it has become common in renderers to refer to reflected light as specular (or sharply) reflected light.
In the real world light does not have a separate "diffuse" or "specular" part. So what makes a surface look dull, or mirror like? It is the smoothness of that surface.
A surface which is not very smooth has tiny imperfections which scatter the light in all directions, thus creating a very "diffuse" reflection of its environment. So it is the reflection of light from an uneven or granular surface, resulting in an incoming light wave being reflected at a number of angles.
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