This is used on a milling machine to find the edge of a piece of work.  The shaft is split into two pieces which are held together by a spring.  The device is gripped in the milling machine chuck or collet, and offered up t the edge of the work, because it is split the device will wobble, when it is slowly pressed against the work edge it will stop wobbling and then ‘step’ out of alignment, this is the exact edge of the work.  You now zero your dials, and add or subract half the diameter of the centre finder, which is usually 4mm or 10mm dia.  The device centre is now exactly over the edge of the work.  Now you have a datum point where you can advance the work to wherever you need to start machining.  Very useful when machining a keyway or drilling through the centre of a bar, or if you are co-ordinate drilling.

I will put up a guide on how to use the centre finder, a video would be ideal.