Parting is the splitting of a gemstone along twinning or pressure planes.
Although this is similar to cleavage, parting can only be done along certain, well defined, planes of weakness and it is not reproducible like cleavage. Usually, these parting planes are created during growth of a crystal when pressure was applied to the crystal causing it to (partially) break or fracture. Later overgrowth then heals the fracture, leaving a weak area inside.
One of the most profound examples of parting is mica which consists of many very thin layers that can be easily parted with the fingernail. It is this mineral that is traditionally used for quarter wave plates.