What evolutionary advantage/ biological explanation could there be for having silver eyes? Tapetum lucidum (eye-shine as seen on cat's eyes) is a possible partial explanation, but these eyes need to actually be reflective, like mirrors.
Off the top of my head, shiny things usually are used to attract prey. Like an angler fish. Or, similarly to bright colors, they're used to dissuade predators, like caterpillars. Hope that helps!
may be it lives (or once evolved to live) in an area where the light conditions could suddenly vary from darkness to extremly bright, and the silver mirror like coating developed to protect the eyes from these sudden changes
Maybe your creature's eyes are capable of "seeing" parts of the EM spectrum beyond the limited wavelengths of visual light? If, say, a creature could see infrared radiation (heat) most forms of cover, shelter and camouflage would be obviated when it hunted. I have no idea why that would make the eyes silver though. I don't know how speculative your idea is, but nearly all the properties of our eyes are defined by the spectral class of our sun. Human eyes are most sensitive to yellow-green colors because our sun is yellow (M class) and radiates a majority of its visual light along those wavelengths. If you're playing around with other planets there's limitless explanations for eye color and abilities. Going to what @big soft moose moose was saying, if this creature originated near a variable star that brightened by several magnitudes on a predictable basis before dimming again, eye protection would certainly be key, though the temperature differentials would cause all sorts of problems.
It could be a reaction to a thermal issue. Its physiology, for some reason, needs its eyes to be cool, so reflecting radiant energy in an environment with lots of sun could protect its retina or both/either rods and cones. In this case, perhaps there is a defect or a natural condition in the retinal pigmented epithelium such that it can't absorb the scattered light in bright daylight, blinding and damaging it over time. Now the mechanics of the eyes will need to be considered. If the eyes are exactly like silver, then no light energy is going to pass through, rendering the eyes useless as sensory input for vision. If you accept Infel's suggestion, then you would have a lure for a blind creature. If you want the eyes to be functional, then it would have to be partially transparent and reflective. A thin enough layer of silver might do that. This is similar to the window coatings on many skyscrapers (which often use aluminium for cost). Your creature would see things a bit darker than you and I would, and night vision would be practically absent altogether.
Or you could simply use the 'get out' of it being an evolutionary sexual selection thang. A physical trait being kindled through the generations, solely on the basis of it being attractive to the opposite sex. Survival of prettiest.
Perhaps those who make eye contact with these creatures are shown the truest reflection of themselves, for better or worse. Sorry if that's too literary, I'm not great with the fantasy/sci fi genres!
