Folding the dough (coil fold, stretch and fold) is a typical step that is found in many homemade bread recipes. The motivation for this step is that it contributes to make the dough stronger. What does it mean? How does this action make the dough stronger? What is the impact on the final result? 
A "strong" dough is a dough which holds together well. Bread doughs and pasta doughs, when compared to other doughs, are strong in the sense that they are not crumbly, but very cohesive. Within the spectrum of bread dough, a strong dough is a dough that feels like play-doh. Right after kneading, it sticks little or not at all, it is elastic (wants to return to its original shape after deformation), and when it rises, it is capable of trapping lots of gas. This is caused by the internal structure of the dough. It is held together by an elastic mesh of a protein called gluten, and when bakers say "strong dough" they mean a dough in which the gluten mesh is stronger than in the weak dough. The mesh is denser and holds together better. The way kneading (including stretch and fold) makes dough stronger is by creating gluten. Flour contains the precursors of gluten, glutenin and gliadin; when they meet each other in the presence of water, they stick together. When enough of their molecules stick together, they form the mesh, in which the starch and other dough substances stay embedded. The physical action of the kneading makes these molecules meet each other and stick together, creating the gluten structure. The stretch and fold technique is used mostly in very wet bread doughs, where traditional kneading doesn't work well. It creates a better-aligned gluten than traditional kneading, because you are always working in the same direction. But I wouldn't call the stretch-and-folded dough stronger than traditionally kneaded dough. 