Sewing on the edge to me is that my sewing is often done around the edges of a busy life and also, no matter what else I do, sewing is always hovering around the edges of it. I sometimes think, or feel, that my sewing to-do list is the real list of my life and there are not many hours that don't go by without thinking about making something.
Also to me sewing close to the edge, as in really good edge-stitching, which is a much finer version, sort of a graduate version of the old basic topstitching a presser-foot-distance-away from the finished edge, really good, close to the edge edge-stitching is a sign of knowing why you are doing what you are doing, which is to flatten and define a folded or seamed edge of fabric.
And those things I finally figure out, or get, are what this blog is about, because if it is news to me, it might be to someone else too.
Oh and by the way the thinner the fabric the closer to the edge your edges stitching should be. For a cotton blouse, really close. For a mohair coat, back it right up, maybe even as far away as a presser foot distance away.