Folding the dough (also called turning, stretch-and-fold, or punch-and-fold) during the first fermentation helps to develop the gluten and increase the strength of the dough. This means that the dough can be worked less during mixing; this is beneficial because excessive mixing can oxidize the dough, which detracts from flavor and crumb color.
The fold involves stretching the dough and folding it in thirds letter-style, then repeating the maneuver in the other direction. The whole process may be done once, twice, or more, usually spaced out evenly through the first fermentation.
I like to ferment the dough in a low, wide container so I can fold it without turning it out onto the counter. This works especially well if the dough is very wet. My video shows me picking up the entire piece of dough for stretching (the second time), but I would not be able to do this with a wet dough. Wet and/or floured hands help keep the dough from sticking to them.
Try to avoid tearing the dough during the stretching; I was not completely successful at this in this video. And the whole thing is admittedly rather sloppy, not a ton of finesse here. But until I can shoot another one, here it is: