Underlay is stitching you never see. It goes down before the visible stitches and does three jobs: it fastens the fabric to the stabiliser so it cannot shift, it flattens pile so the top stitches sit on the surface, and it gives the top stitching something to grip.
A design without underlay is where gaps come from. The outline sews, the fabric creeps a fraction under the needle, the fill sews, and now there is a sliver of fabric showing between them.
A single line of running stitch just inside the edge of the shape. Cheap, about as few stitches as underlay can use, and it holds the border of a satin steady. This is the default for satin columns and for anything on light woven fabric where a heavier underlay would itself cause puckering.
A loose zigzag up the middle of the shape. It holds the fabric across the whole width rather than only at the edges, which is what stretch fabric needs. Use it on knits, jersey and performance fabric, and under wide satins.
A sparse fill under the fill, usually at right angles to the top stitching. The heaviest option and the one that flattens pile: fleece, towelling and thick knits. It costs stitches, so it is not the default, but on a towel it is the difference between a readable design and a fuzzy one.
Underlay stacking is a real fault. A centre walk, plus a zigzag, plus a tatami, plus the top fill puts four needle hits through the same piece of fabric, and that combination breaks thread and stiffens the garment. One underlay type is normal; two is occasionally justified on pile; three is a mistake.
It stitches the fabric to the stabiliser before the visible stitching goes on top, so the fabric cannot shift or sink. Without it, outlines drift away from fills and stitches disappear into pile.
On firm woven fabric with a small design you can often get away with it. On knits, fleece, towelling or anything that stretches, skipping underlay is the usual cause of gaps and sunken stitches.