What is the purpose of folding/toweling my no-knead bread?

You probably want to read the bread chapter in Harold McGee's http://www.librarything.com/work/44636.

(This is my opinion, I'm not a trained baker.) I think the folding of the dough is to create a seam. You know how breads have that slash on top? When you plop the bread into the hot dutch oven, the recipe tells you to do it so the seam lands face up. As the bread is baking, the seam provides a gash where steam can escape. As for the towel, I think it's to not allow moisture or foreign particles in. I don't know. I've never really questioned the towel :) I'm interested now as well!

The reason it's possible to make bread with wheat flour is because of a protein called gluten. Gluten is very long and isn't folded-and-hooked like a lot of proteins, but initially it's kind of tangled up. The kneading process used in dough straightens the gluten out and aligns lots of gluten molecules the same direction. That's the difference between "bread" and "biscuit" (as Americans use the term). The "folding" you're talking about is actually the same as kneading, and its purpose is to straighten out the gluten, at least somewhat.

It helps it develop the crusty-crust/softy-insides when it bakes, without developing an unpleasant skin-crust while it rises. If the bread gets the skin-crust, it gets trapped and it can't rise anymore, but if it's covered in plastic, the whole surface stays completely pliable, and becomes a thin, soft crust when it's baked.

(My response is for the towel, sorry I wasn't specific!)

Gluten is the reason why you have to be really careful how much mixing and stirring you do when you make biscuits. If you do very much, the gluten starts to straighten out, and then your biscuits will be chewy and bready instead of flakey and soft.

Where I come from, we tend to cover things with a tea towel to keep flies out.

Yes, folding is a way to get long, aligned strands of gluten, as well as deflating the largest gas bubbles, without working the dough very much -- this lets you have a wetter dough than you could knead.

It's a way of adding structure. I don't know that it's critical on this kind of loaf since it's contained in a dutch oven, but on more traditional loaves, the tension of the gluten helps the bread rise upwards instead of spreading out.