Sure, glad to. The majority of the malt sugars should be converted to alcohol in the primary.
During the secondary stage clearing, mellowing and blending (balance) take place, but hardly any fermentation (if done right).
When we prime we are adding more food for the yeast to convert.
If we left the brew in an open container it would just ferment out.
After priming and racking to a closed container, bottles or a keg, the same fermentation takes, but the CO2 gets absorbed into the liquid which creates carbonation. This takes approximately 3-4 weeks, depending upon temperatures.
If we ferment the brew all the way out then there should be no food to produce carbonation in a closed container so priming sugar must be added. If not, it may take 6 months or more to become carbonated.
Incidently, I have a German recipe for a Kellerbier that doesn't mention priming at all. I think it depends on gravity at kegging time...like this next paragraph.
If you are a good planner you could keg before the fermentation is complete and would not have to prime. But the question is, when is that time? At what gravity do you do this exactly? If you are expecting a FG of 1.010 do you rack to a cask at 1.012, 13, 14, 15, 20? I do not know myself, but it does make me curious to read that recipe again...it mentions different days for several stages than 10 weeks. Sounds more complicated than it really is, I'm sure.
So, we, as "patient" homebrewers tend to let it ferment out all the way and prime when we bottle. Of course with kegs you'd gas it.