Pad stitching is a means of joining two pieces of fabric together. In the context of tailoring, it's used to join a relatively stiff, non-fusible interfacing (like the one you see above) to the lapels or collar, with the aim of shaping the fabric to 'roll' nicely and keep it's form.
I generally tend to use horse hair canvas as my interfacing of choice in this application - which is also known as 'hymo' or 'hair cloth' (which in times gone past was actually made out of either horse or camel hair, but nowadays is generally a blend of wool and goat hair).
The pad stitch is applied to the collar or lapel piece which will be underneath the collar or lapel - so the stitches aren't seen (If you're skilled, you can do it so they don't show at all). You keep the pad stitches outside the seam allowances, so when you're finished, you can sew the top and underneath sections of the collar or lapel together and no-one but you will know what's hidden underneath.
In this explanation, I'll be showing you how to do the stitch only - its best to discuss the types of interfacing when in context of its use, as each tailoring project is different. There are numerous ways to do the pad stitch - I rather like my pad stitches to form 'chevrons'.