A bench pin makes it easier to hold wood and metal when you cutting it with a piercing saw or jeweller's saw. Here a simple wooden bench pin is clamped to the work surface so that the handle of the jeweller's saw (or a fret saw) can be drawn cleanly up and down or at a very small angle to the work. The worker uses their hand to hold the piece on the bench pin, while carefully drawing the saw smoothly up and down to cut. The supporting hand is not shown in this photo or you would not be able to clearly see the blade.
You can use either the V or the hole in the bench pin as the area where you work the saw blade, the work is turned slightly on the bench pin as necessary to make curved cuts (you don't move the saw around, but rather gently adjust the work.)