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.<p>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.<p>The big picture: The purpose is to modify user behavior toward actions that improve or at least are less detrimental to HN.
What brudgers said is correct, but I'll add that we're probably going to get rid of comment averages. We've looked at the data extensively and it hasn't proven to have much value. We've phased out the code that used to rely on it, and what's left (which is only for display) is probably not worth the cost.