I think it was Icon who wrote a very good description here a while ago. It went something like:
Imagine precision as a circle surrounding the point you aim at. The ball can land anywhere within that circle on a dinged shot. High precision clubs have a small circle, low precision ones a larger circle. Where you land in this circle is pretty much randon, even when you hit the ding.
Forgiveness can also be seen as a circle surrounding your point of aim. This circle is where the ball might land when you miss the ding, high forgiveness = small circle, low forgiveness = large circle. Where you land in this circle is determined by which side you miss the ding. Miss left = goes left, miss right = goes right.
This is why when you miss the ding the shot might still go where you aimed it. Say the ball is going to the left side of the circle of precision and the right side of the circle of forgiveness when you miss the ding right. The result is it goes straight.
In rare circumstances a shot where you miss the ding slightly right might still go left. If your circle of precision is large (low precision clubs) and your circle of forgiveness is small (high forgiveness clubs) you can get more variation from your precision than forgiveness if you only just miss the ding. The ball is going slightly right because of missing the ding to the right but the lack of precision is sending it further left resulting in a rather unexpected shot.
Wow, this sounds like utter mumbo jumbo! Icon somehow made it way clearer. Hope it still makes sense.
And I'm not drunk. Honest.