Thank you for your reply .There are two questions here.
Visible light -indeed any light - is the product of an emission process from matter that generates radiation. There are two of these processes: spontaneous and stimulated. Spontaneous emission does not require radiation to be present - it is just given off by matter in an excited state. Stimulated emission is radiation given from matter in an excited state when pre-existing radiation interacts with it. A famous example of this is the laser.
However your first question is what makes certain wavelengths of light visible to us. That is the result of the electrochemical signal produced, when light in the range of wavelengths our retinas are sensitive to strikes it. The sensitivity range is determined by the photochemistry of the retina, specifically the "photopigments" present in the light detection cells of the retina.
So this is to do, not with how light is emitted but how it absorbed, in the eye. I do not know exactly what happens to these photopigments after they absorb a photon of the right wavelength, but I imagine they will produce an excited state of the pigment molecule, which will then release its energy, somehow, in a chemical form that is ultimately converted to a signal in the optic nerve. (I am not a biochemist.)
How does the appearance of an object, its colour and shape, transfer itself to a mirror?