Dough strength?

...dough strength means how developed is the gluten structure.  A more developed gluten structure means the dough will hold itself together better and if you were to stretch it, it wouldn't readily rip or tear (i.e. strong).  It's easy to identify a weak dough because as soon as you start to pull it, it tears in long strands.

Folding the dough usually entails the stretch and fold method.  To do this you want a "strong" dough so that when you go to stretch it, it doesn't tear. 

When letter-folding you want to be able to fold the dough over itself without it ripping or tearing.

When using the slap-and-fold method you usually start off (not always) with a shaggy mass that has poor gluten development.  Right away you notice that it sticks everywhere and when you try to pick it up only bits of it come up with you.  This dough at the beginning is weak.  After a while, though, more gluten starts to develop and when you pick up one side of it the rest of the dough comes up with it without tearing.  This dough is strong.

In many cases the higher hydration doughs with have a very well delevolped gluten structure and stretch very easily.  In my opinion they strethch better than the lower hydration doughs.  But depending on what stage of the fermentation process you are at, you do want to be gentle not to deflate the dough too much.

A strong dough will hold its shape better than weak one and potentially rise to higher heights. After a number of folds the dough will hold its shape better. So if a dough is already strong it will require less folds and will likely resist them.

If you really want to get a good grasp of what dough strength is then you should read, http://www.sfbi.com/images/pdfs/NewsF04a.pdf