WHAT IS A "QUILTING STITCH" ?

The "quilting" stitch is actually pretty simple, even historically.  Remember that no matter how pretty (or not) the actual quilting is on any quilt, the stitching serves a real purpose: to hold three layers of fabric or fibers together. Someone far back in history discovered that 3 layers were warmer, or lasted longer, than a single layer of fabric.

A quilt is three layers - think of a sandwich:

• Top (today usually some form of patchwork or applique). Historically it could be a single very expensive or beautiful fabric (in today's world known as wholecloth)
• Batting (wadding or padding for the British) which can be wool, cotton, or some other fiber made as a continuous piece or small pieces laid overlapping on the backing to form a thicker center section. The quilt stitching will keep it in place so it does not shift around or bunch up.
• Backing is the fabric that is used for the back,  or underside, of the quilt.  It can be pretty or not, it can be the same fabric as the top or coordinating fabric, or it can be some fabric that is around and usable with no real matching connection to the top. 

According to Colby (Quilting by Averil Colby,  published 1971, pg. 169-170) there are two stitches used for actual quilting:

Back stitch - "this is used only if the batting is very thin" and "not visible on the back, such as a cushion".

Running stitch - "...commonly used for bed quilts, garments, or anything for which a fairly substantial layer of padding for warmth is needed."