When you are making a portrait of someone, you certainly want to do everything you can to make the photo stand out. Keep in mind that little things can help your photo look better, even if the viewer isn't consciously aware of why he likes it. One of the techniques to learn is adding catchlights. Catchlights are reflections in the eyes (usually of the main light source). They add depth and dimension to the eyes - a spark that will draw your viewer's attention.
Catchlights are created by reflections of light sources, derived from nature, studio lights, flashes, or reflectors. They can be small or broad, focused or blurred, rectangular or circular - all depending on the light source that causes them. There are many photographers who study the positions of the catchlights and will use them to influence the viewer's feelings about the model. Many photographers have created their own "rules" to tell you where you should put the catchlights. The most frequent rule I've seen: catchlights should be positioned between nine and twelve o'clock. (I'm not a strict adherent of these rules, but they are, usually, a good starting point.)
I have seen several training sessions showing how to enhance or create catchlights in post-processing software. Yes, some photographers consider those little catchlights that important. Viewers may perceive a person without catchlights as lifeless, or even evil.
OK, we know the jokes are lame, too.
Of course, you can still make good portraits without a catchlight. Keep in mind, bringing lots of extra equipment or spending lots of time positioning yourself or your subject to guarantee great catchlights may cause you to miss a photo. Your subject might not want to cooperate. You can't always run up to a spontaneous subject and shove a reflector in his face.
If you are out making photos in a less-than-formal portrait environment and still want some catchlights, bring a flash. If you use some kind of dome diffuser and power the flash way down, you'll get a little fill light on the face and catchlights in the eyes. You'll be surprised at how natural this looks, if you keep the flash power very low. Outside, you can point the flash straight up, and your dome will still provide enough light to reflect in the eyes.