I've heard them called leaders and enders, starties and stoppies, and spiders (because of all the "legs" sticking out of them after they have been used a while). I think the most important reasons for using them is to prevent the fabric from being pulled down into the needle hole; to save thread; to prevent thread bunch-ups when you start to sew; and to prevent the needle becoming unthreaded with a little brush from something-anything. And you don't have to waste time hunting for both those ends to hold onto them.
I was taught the fabric needs to be several layers. I use about four, and there is always one under the presser foot with the needle down when I walk away from my machine. . . well most of the time. LOL