This guide bush for 5/16 inch lamp augers has a special large side hole which makes lamp drilling a pleasure. As the auger is withdrawn from the wood the shavings can fall away through the hole so the auger does not have to be withdrawn all the way out of the tailstock to clear the shavings every time. Also it saves dust getting jammed inside the tailstock barrel.
The centre pin is used as a centre finder but as it is precision ground hardened steel with a 60 degree point it can be locked in place with the grub screw and used as a tiny tailstock centre to support the end of small projects, allowing easy access for the tools.
This has a 1 Morse taper but the image is of the 2 M.T. version.