Mirrors are the best reflectors of light that human ingenuity has been able to devise. Notice, however, that the light is reflected only from the backing of the mirror, after passing through the front layer of transparent glass.
What is there about the backing that makes it such a good reflector? It’s a thin, smooth layer of silver metal. All metals are shiny, or reflective, because their atoms are held together by a sea of loose, swarming electrons that have no affiliation with any particular atoms. That’s why metals conduct electricity so well, because electricity is just a movement of electrons.
The swarm of footloose electrons in the silver, belonging as they do to no particular atoms, have no particular preference for absorbing any specific wavelengths of light, so they reject and reflect back all wavelengths.
Of course, a sheet of shiny silver metal would make a fine mirror without the glass, but it would quickly tarnish.