Pulling the back to the front for binding is harder then you think. You can get tunneling of the fabric which makes it difficult to get a nice sewn edge. It looks like the sewing was not done very well and it let the edge of the fabric fray out. You can either undo the sewing and see if there is enough binding fabric to come over and enclose the frayed edge or patch the edge first or put on new binding. Quilt seems to be in good shape otherwise and redoing the edge should make it last a while longer.