Without this layer of canvas the strain of the buckles (or whatever you use for fastening) will strain the pleat stitches. I use a 3" wide strip of plain old cotton canvas in my washable kilts. Wash it several times in hot water so it won't shrink later, and be sure that it is loosely stitched to the pleats and tightly fastened to the inside of the kilt beneath the buckle straps. That way as you cinch down on the straps the canvas is taking the strain and not letting it translate to the pleat stitching.
Think of it like the inside of a hard hat. The harness grabs your head and the helmet just goes along for the ride. In the kilt, you're actually cinching the canvas around you waist and the kilt just goes along for the ride.