Stay stitching is an important preliminary step to constructing your garment. A stay stitch is stitching along a raw edge of a single pattern piece in order to prevent stretching or neckline or armhole.
It ins't uncommon to skip this step when you are more experienced with a particular textile or garment, but it is definitely a good idea to stay stitch when you are constructing something for the first time, or are deciding to design/self draft your own pieces. This will allow you to critique your pattern without external factors such as fabric stretching affecting your future changes you may make to your pattern.
There are a couple reasons why you want to stay stitch in terms of fabric behavior. Typically this step is done to a curved edge of an arm hole or neckline. Curved edges of a garment will be cut on the bias, which means that edge will exhibit the characteristic of easily stretching. You want to counteract that characteristic so that your garment doesn't warp/stretch as you are constructing the garment (there is a lot of manipulation to the fabric when constructing a garment, I have had pieces stretch over an inch along a neckline, which is very problematic when applying a collar or collar stand).
Stay stitch within the allotted seam allowance of your pattern. This stay stitch is stitched 1/8 inch from edge. I prefer to use a 3mm stitch length when stay stitching (a tad longer in case I need to seam rip or use to the stitch to ease fabric by subtly gathering together if I want a curved edge of a armhole to lay a slight different way).
STAY STITCHING HACK
Stay stitching is another one of my least favorite sewing steps. I recently started stay stitching after tracing out my pattern and before cutting the curved necklines/armholes. These tutorials I traced in a thick sharpie for you to see easily.
Stitch 1/8'' from edge of cut line along necklines and armholes.
I start v-necks at the center front and work my way to the shoulders to keep the process as symmetrical as possible.
No matter what stitch you are doing it is always a good idea to hold down the thread tail as you stitch your first stitches. Do not back tack on stay stitches.
You now have a stay stitch right next to your cut line.
Now cut your pattern curved lines.
An added bonus of stay stitching, is you can use this stitch to pull in any subtle gaping on underarms or necklines (great hack to make a pattern work that could ultimately benefit from some fit adjustments).