JOJO, Dodging and Burning was something we used to do under the enlarger lens in the old roll film days. We used our hands, fingers and paper card cutouts to hold back areas that were over exposed (Dodging), and increase the exposure of areas that were under exposed (Burning).
It is much easier with digital because if you don't like the result you can undo it. Couldn't do that with sensitive papers.
Here is the before and after of my Oak Tree. I Dodged the left side of the trunk and the branches which were too dark, and Burnt the sunlit area to bring back more of the detail in the carpet of leaves. I also softened the white fence that was too strong in the original. I DID also boost the saturation a bit....
These adjustments are usually quite subtle to just improve the range of colour or tones. I hope you can see the difference, things don't always transfer very well.

I agree with Horus ref The Gimp. Can't do layers but you can do most other things and it's a freebie.
