Eyes show up a lot in Blade Runner. We get to see the fake lenses shining in the eyes of the replicants—and in the eyes of an artificial owl. We see the hellish L.A. landscape reflected in an eye. And we see Roy and Leon take a trip to the lab of a dude who designs eyes (and who made their eyes, specifically), where Roy comments on the subject: "Chew, if only you could see what I've seen with your eyes!" (source)
Maybe the reason eyes come up so frequently is because they're traditionally thought to be the "windows to the soul"—they're the main organs we have for experiencing reality. Whereas the humans treat the replicants as though they were just machines or tools, which can be "retired" without ethical compunction, they actually experience reality in a rich and conscious way—their eyes aren't empty.
In a lot of ways, Roy seems to be more alive than many of the authentically human characters. When he talks about the things he's seen with the eyes Chew has manufactured, he's really talking about how astounding his experiences have been, and he's denying the notion that he's just some lifeless automaton.
There's also the Voight-Kampff Test, which measures the fluctuations of the subject's iris and pupil in order to determine whether he or she is a replicant or not. This strikes at the heart of what makes humans and replicants different: the way the replicants see the world, in emotional terms, isn't "normal." They'll end up feeling empathy for oysters before they feel empathy for dogs—things like that. (The shining lenses in the replicants' eyes also highlight the fact that the replicants are perceiving things differently.) But the false memories Tyrell has given Rachael help her have more or less normal reactions, seeing the world in a way closer to the way humans perceive it. So what makes her different from a human?