Not better focus, but it provides quick access to options on a camera that fully supports it. You get a lot of control over focus. Your main mode is af-c. You hold the back button down and the camera keeps on focusing. Great for following sports players, etc. In other situations, you focus with the back button on whatever you want, then release that back button. Your camera stays at that focus point. Good for focus and recomposing, but it goes far beyond that. Its good for anticipated action, pre-focus on a basketball hoop and you are ready for the shot and can frame it however you want when the moment happens because the camera is already focused on the hoop. Lots of situations where that is helpful.
Here is an article, first one I came to, there are tons of examples on the web. But remember, your d3100 cannot do release priority mode.
Back Button Focus: What it is, why you want it & setup guide