This was copied from Claire Shaeffer's Fabric Sewing Guide "The strongest hand stitches, backstitches are used to sew and repair seams in hard-to-reach places, under-stitch some fabrics and couture designs, set zippers by hand, and complete garments when a machine is unavailable. Working right to left, secure the thread. Take the stitch 1/8" to the right of the thread, bringing the needle out 1/4" away, to the left. Take the second stitch by inserting the needle at the end of the previous stitch. Make the stitches longer or shorter as desired." There are 8 stitches/inch in the directions above. For a stronger seam, make the stitches closer together. The stitches on some Worth gowns were about 1/16". Many bespoke tailors use this stitch for the shoulder and armscye seams. The backstitch can be adapted for half backstitches, prick stitches, and pick stitches.
This is the most important stitch out there, isn't it Claire? I use it wherever I can't imagine making the machine go. It is as solid, and more adaptable.
The backstitch has more elasticity than running and machine stitches. This makes it ideal for some seams. I agree it's perfect when it's difficult to machine stitch.