Jump rings are those little loops of metal that hold jewelry together. There are hundreds of them in the woven chain collar project, and at least a few in most jewelry projects. Opening and closing them the right way will make your project work easier and it will keep your jump rings stronger. The more you bend metal the weaker it gets, so this technique maximizes how open the jumpring is (making it easier to loop through other things) while minimizing how much you have to bend it. It's also the easiest way to get it closed neatly.
When you open or close a jumpring you want to twist it. If you were to pull the pliers apart (left and right in the images above) you would create a bend point at the other side of the ring. That bend point will forever be a weak point in your design, more likely to fail than any other place on the jump ring. By twisting it open and closed (up and down in the images above) you don't create a breaking point, and you reduce wear and tear on the ring.
A properly closed jump ring has both ends meeting. Your goal is to make a perfect circle. You don't want the ends to overlap in any way. Just a neat, closed circle.
It may seem like a small difference, but it amounts to a lot. You only need one jump ring to break for most jewelry to become unwearable until repaired. It's always a good idea to practice good habits when you're making things, and this is an easy one to implement!