Stay stitching is a single line of stitching, through one layer of fabric, to stabilize the fabric, preventing it from becoming stretched or distorted. Stay stitching is usually called for on the edge of a piece of fabric that has a bias cut to it which would allow the fabric to easily become distorted.
Now I realize most outer edges of quilts aren't on the bias or curved but trust me on this. Stay stitching takes me back to my garment sewing days. And trust me, if a pattern called for stay stitching, take the extra time and do the stay stitching. So trust me on this with your quilts too.
Stitching around the outer edge of your quilt, particularly those with a pieced border or a quilt top with no borders will increase the likelihood that the quilt will be square. As the definition goes, it prevents it from becoming stretched or distorted.
So how do you stay stitch around the edge of a quilt? It's really quite simple. I sew through the single layer of the quilt top, a scant, scant 1/4" from the edge. When I say a scant, scant 1/4" I mean that I move my needle position to the right as far as it will go and then stitch around the perimeter of the quilt. I allow the feed dogs of my machine to feed the quilt through and stitch the line. I simply just guide it with my hands being careful not to pull on it or force feed it. I leave my stitch length on the normal length I would stitch the quilt together with (on my Bernina 1130 machine it's set on 2).
It really only takes a few extra minutes to do this but it will make your longarm quilter's life (or yours) so much easier and she will love you for it!