The crown of the barrel maybe the most important "key" ingredient to accuracy. Crowns are usually recessed in order to protect them. However they do not have to be recessed. As long as it's square to the centerline so that the bullet is released evenly, free of the bore then life is good. If the crown is not even then the bullet can be cocked by the high pressure gasses as it clears the muzzle. if the crown gets nicked this will create a drag on one side of the bullet as it tries to exit the muzzle, causing the bullet to be cocked off of centerline. A good "for instance" is a gun that is normally shooting straight on suddenly starts shooting low and right. Look straight onto the muzzle for crown damage lower left.
One good reason to run your cleaning rod from the breech is to prevent uneven wear on the crown.
Crown of threaded muzzle can be damaged especially if the treaded attachment is removed.
In short, What defines crown damage? Anything imperfection that causes the bullet to exit the bore unevenly.