Mechanically: At one time, and perhaps still, it appeared to affect decay rate and placement of a person's new comments. For example, a person with a high average comment score might have their initial comment placed higher up the page and then fall more slowly than a person posting at the same time with a lower average comment score.
As Feedback: Because it is a moving average, it is a way for a person to get a feel for the quality of their comments and how that quality is trending. That's really more important in the long run I suppose.
The big picture: The purpose is to modify user behavior toward actions that improve or at least are less detrimental to HN.