What happens to pasta dough when it is run multiple times through the machine? Before, when I made fresh pasta, the dough would become a little "brittle" and was hard to work through the thinner settings of my pasta machine. Then I saw a tip on a cooking show to put the dough through the thickest setting several times (about 6 to 8 times), each time folding it onto itself. 

The reason given in the show for the tip was that it would improve flavor/texture of the cooked pasta. However, it felt to me as if the dough became easier to handle (less "brittle") as well.

My question: what happens to pasta dough when you run it through the machine on thickest setting multiple times?

Some research I did before asking (that didn't give me an answer yet):


Remembering it may have something to do with gluten, I read through the Wikipedia article on gluten. It does mention elasticity in the "bread" subsection, perhaps the same thing is at work here? 
Searching this Stack Cooking site I found this highly upvoted answer which mainly mentions gluten's effect on "elasticity" in the context of "chewiness", but doesn't related it to how well the dough can be handled.
Of course I tried to Google the answer, but that mainly results in recipes for fresh pasta.
You're alluding to the correct answer:  running it through several times basically kneads the dough and develops gluten. 

Gluten provides strength to dough.  It forms a flexible, elastic 'net' (the 'net' portion isn't really relevant to pasta dough though) , allowing it to stretch more and is much, much less brittle.  Even better, would be to put it through several times, then let it rest for a few minutes so that the gluten relaxes and then continue.   

You could also simply knead the dough longer.  Many pasta doughs are extremely dry and very difficult to knead by hand - so the kneading mainly happens at the roller stage.  If you're using a good mixer or feeling especially hulk-like, then you could knead further by hand.