Cleavage.
The tendency of a mineral to break along smooth, flat planes determined by its internal atomic structure.
Cleavage is how a mineral chooses to break. Inside every crystal the atoms are bonded more tightly in some directions than in others, and when a stone is struck the break tends to follow the planes where the bonds are weakest. A mineral with perfect cleavage will split into smooth flat sheets or blocks. One with poor or no cleavage breaks unevenly, in what is called a conchoidal fracture (the curved shell-like surface seen in obsidian or flint).
Cleavage matters in practical ways. Mica has perfect cleavage in one direction, which is why it peels into thin transparent sheets. Fluorite has perfect cleavage in four directions and breaks into octahedra so neatly that the offcuts are sold as tumbled "octahedrons." Feldspars, including moonstone and labradorite, have good cleavage in two directions, which is why a hard knock on a corner can produce a sudden chip.
For anyone setting stones in jewellery or simply storing a collection, cleavage is the property worth respecting. Stones with good cleavage want padded storage and gentle handling. Hardness alone does not tell the whole story.