how wide you cut the strips for the binding will be determined, in large part, by how wide you want the finished binding to be. The "formula" given my by my early quilting instructors is: For a folded (double layer) binding, determine width of finished binding then multiply by 7 to determine width of strip to cut. Example 1 - for one quarter inch finished binding: 1/4 times 7 is 1 and 3/4 inch cut strip. or..for half inch finished binding: 1/2 times 7 is 3 and 1/5 inch strip.
From a practical standpoint, this formula works well if you're hand stitching the final binding seam. Since I don't do handwork I've adapted that formula to accommodate machine stitching the final seam...but there's a different discussion thread on all that.
Why would people do different widths of final binding? In my case, just for the look of it. I prefer a bigger binding on a bigger quilt...