Dodging, with no "e" is the process of lightening selected areas in a photo; originally dodging was done under an enlarger's lens, by hold back or "dodging" the light, using a thin wire and a shaped piece of posterboard or cotton ball, etc, or by using one's hands to "hold back" the light, in order to lighten selected areas. BUrning in was often done with the hands, making various sizes of openings with your hands, or by using burn-cards or "vignetters"...burning in is the opposite of dodging.
Today, dodging can be done in image editing software, and it still refers to selectively lightening areas of an image.
The thirds rule is called more properly the "rule of thirds"; a quick Google search ought to give a good definition of the rule of thirds in something like 2,000 or so articles.