I get this question- frequently. So, I am going to post an answer, HERE, where everybody can find it.
First, a knitting sheath is a tool like a knitting needle. Just as there are different kinds of knitting needles, there are different kinds of knitting sheaths. And, just as there are different techniques of knitting there are several different techniques of using a knitting sheath. The most common knitting sheaths can be used while tensioning the yarn in either the right or the left hand, or with a strand of yarn in each hand, or with two strands of yarn in either hand.
A knitting needle is a lever for moving yarn. In most modern knitting techniques, the mechanical advantage is about 1: 3, with the fingers/ thumb of the hand providing both the force and acting as the fulcrum of the lever. This places stress on the hands and wrists. When the needle is inserted into a knitting sheath, the knitting sheath becomes the fulcrum and the force is applied with a 1:50 mechanical advantage. In addition, the knitting sheath allow the forced to be generated by the large muscles of the shoulders and transmitted through the very strong tendons of the upper arm.
With a knitting sheath or stick tucked into a belt or apron strings under the right elbow, and a fairly short working needle set it, The needle is pushed sideways into the working stitch with the palm, the yarn for the new stitch in any one of half a dozen ways, and the base of the thumb pushes the working needle out of the stitch, finishing the new stitch and transferring it to the working needle.
Gansey needles act as springs. One end is firmly anchored in a knitting sheath, and the needle flexed under the right arm. The weight of the arm pushes the needle tip into the stitch, and as the arm is lifted a bit, the needle springs upward, finishing the stitch and pulling it onto the working needle.
In swaving, (terrible knitting) a short curved needle pivots in the knitting sheath, and the yarn tension is controlled by the left hand. The blunt needle is “popped” into the stitch with a symmetric downward and outward push with both arms. The forward leg of the old stitch and supporting fabric act as a spring. The needle catches the yarn with another “pop”, the force of the arms holding the stitch open is relaxed and the spring of the yarn in the old stitch pops the needle out of the old stitch (still carrying the yarn) to form the new stitch on the right needle. (I have not mastered swaving yet and there may be changes to this in the future.)
Knitting sheaths are tools that provide leverage, just as hammers are tools that provide leverage. You can drive a nail by holding a lump of iron in your hand, but using a hammer is easier. You can knit with hand held knitting needles.
That is my story, and I am sticking it until I get better data.