I noticed that the most common compliment a photographer receives is along the lines of "You have a good eye." I find this interesting since it is unique to photography and doesn't really correlate to any other artform (you don't tell a sculpture you like their chiseling or their hand-work). The question is "Why?"
A good part of the reason would be that, while anyone can go out and take a photograph, the way an individual photographer approaches a scene or subject is unique, especially when considered over a large selection of photographs. So, appreciating a photographer's "eye" says you like subject the photographer chooses, or at least the resulting photograph.
The ones that I find more interesting come when you see a photograph who's subject matter is not something you generally like or may not have even seen before. These are the rare images that can change the way you see the world or the possibilites of what a photograph can be. They inspire in ways that are lasting and meaningful.
The photo below was inspired by many drawings or paintings I've see where a vision is shown replacing the iris in an eye (a skull foreshadowing death or something else implying the future). I decided to see whether something similar could be done with a photograph. The image was taken with a macro lens and the camera sitting on a tripod in front of me. What I discovered is how reflective the eye actually is and how interestingly it reflects "reality". It is a visual representation of the "eye" of a photographer.