The bit that rotates is called an armature - the piece on the armature that the brushes bear against is called the commutator.
I have been messing with motors on and off for over 50 years and had not heard of the stone you mention until now.
Research shows me it's called a commutator stone and its purpose is to clean up the commutator. In the past I have only ever used fine grade abrasive paper and Scotchbrite scourers to do this job.
Carbon dust can clog up the insulated gaps in the commutator - an old toothbrush and a fine screwdriver can be a useful cleaning aids.
If the motor runs with lots of sparks then you need to pay it some attention - a few tiny sparks are normal.
http://weldingweb.com/archive/index.php/t-80281.html
http://www.sportsmith.net/faq.aspx?ID=164a8165-e847-41db-b83c-36c983b6fa18
I bed brushes in by just running the motor - the important thing for me is to have a clean commutator.
Peccavi, April 2013