To be very simple, HD voice makes everything better. HD voice call delivers twice the sound of narrowband one, so there is much more information provided for the brain to process. Although it sounds like a bad thing, actually it's the opposite. Having more information to process, brain is able to get a better comprehension, and lot less fatigue. Another advantage of HD voice is better accuracy on computer-based processes like voice recognition and speech-to-text.
Advocates and marketers of HD voice are emphasizing the quality of sound, the fact that it is almost like you are talking to someone in the same room. But, to be honest, there are many more reasons for wideband goodness. It is really a wide range of advantages, from being able to understand even a three year old (higher voices get clipped) to public safety. Click the sound samples below to hear the difference.