The teeth of the gears get thicker as you get toward the base of the tooth. The backlash is actually the space between the teeth of the pinion and the teeth of the ring. Backlash is adjusted by moving the carrier assembly, and ring gear, left or right in the housing, making it sit closer to or farther from the pinion gear, until you get the space between their teeth in a given optimum range. If you are still having trouble visualizing what is being adjusted and how, hold your hands in front of you, fingers spread apart and tips facing each other. Now move your hands together so your fingers go between each other and watch the effect on the visible gap. The orientation is wrong, but the effect is the same.
These clearances are measured in thousandths of an inch, and cannot be judged by feel unless you are very experinced (I do work with a guy who can grab a ring gear, rock it, and consistently tell you what the backlash is to within .001"). This number is also critical because too tight will bind up the gears and make them wear prematurely, then make noise. Too loose and the slapping of the teeth as the space is taken up going from drive to coast and back will tear the assembly to pieces. Whenever you see pictures of a diff with whole teeth stripped off the ring it is usually from excessive backlash. Partial teeth stripped off is from insufficient pinion depth.