How does it lock in position?
The simple answer is friction. The finer thread on the head portion of the adjustment helix means that any pressure applied to the clamp head will be translated axially, with a wider and more frictious pressure between the two thread planes.
Inversely, the adjuster portion of the auger has a far coarser thread giving it a steeper angle. This means more pressure is translated laterally, relieving friction and allowing the adjustment block to "slip" along the auger, turning it and moving the head accordingly.