What does pillowcase and knife edge mean?

pillow case is where you sew the quilt sandwich right sides together leaving an opening so you can turn it out. You use this method instead of binding the outside of the quilt. Usually you would then top stitch around the edges of the quilt and hand sew the opening shut...
I am not sure what knife edge means? Maybe ironing something so the crease is really crisp and sharp?

Not sure but would be interested to know.

Oh, Amma, I didn't know that about the pillow case term. Here it's called 'Bagging out'. I think your term sounds nicer.

I've heard of knife-edge pillow and pillow forms, where the edges are very sharp, as opposed to say, box-edge, where the edges are square.

Sometimes too they refer to the pillowcase method as birthing a quilt, too...I think Eleanor Burns may call it that???

Just found this online at http://hartcottagequilts.com/vintage

Vintage/antique quilts are finished in three ways: with a separate binding (particularly on curved-edge quilts); by wrapping the backing around to the front or vice-versa; or (rarely) with a "knife" edge, folding under the raw edges of the front and back and invisibly stitching them together.

The first two finishes can be done at home by hand or machine, but because the edge of the quilt is finished after it's removed from the quilting frame, a "knife" edge on a homemade quilt can be done only by hand.

Instead of "pillow case" we here call it "birthing" Bringing a large object through a small opening.

In the August 2009 issue of BH&G American Patchwork & Quilting magazine, an antique quilt is featured that is finished with a knife edge technique, and they give some instruction for it (quilt is on Page 43, instructions are on Page 48.)

I use the pillowcase method when making Linus quilts. It is much faster and a lot less work than putting on an individual binding. I actually sew that pillowcase method on my serger and then tie or machine quilt.
I was involved in a quilt documentation project at least ten years ago in our county. We saw a lot of antique and just old quitls done with the knife edge method. The batting was usually paper thin and the hand stitches required for that method made it almost invisible. I doubt if many of us are willing or able to do that fine a work. I worked for about 18 months in a shop that did alterations and custom dressmaking. More than 50% of their business involved bridal work. I often ended up doing a lot of very delicate handwork because I was a handquilter and was used to working for long periods of time with very small needles and handstitches.