A key application of dodging and burning is to improve contrast (tonal reproduction) in film print-making; today this is better known as tone mapping in digital photography – see high-dynamic-range imaging.
The technical issue is that natural scenes have higher dynamic range (ratio of light to dark) than can be captured by film, which in turn is greater than can be reproduced in prints.
Another way to prevent obvious cover-up lines is to use slightly less opaque material closer to the outline to produce a more subtle, faded effect.
A card or other opaque object is held between the enlarger lens and the photographic paper in such a way as to allow light to fall only on the portion of the scene to be darkened.
A card or other opaque object is held between the enlarger lens and the photographic paper in such a way as to block light from the portion of the scene to be lightened.