In photography, the little reflections in someone’s eyes are called catch-lights; without them, the eyes can look dull and uninviting.
Even if they’re small, catch-lights can breathe life into a portrait.

Which image do you prefer? I removed the catch-lights in Photoshop on the left image.
If you look closely at the catch-lights, you can also dissect the lighting the photographer used.
Zoom-in and you can see the size, shape, and brightness of the reflections of the lights in the eye.
If you could zoom far enough in to all of my photos, you would probably see my reflection in every single one.