Cleavage planes are common in crystalline minerals. They tend to follow weaker bonded lines through the crystal matrix, and lend a characteristic appearance to many minerals when they are fractured naturally or by a mineralogist.
The art of diamond cutting exploits the many possible cleavage planes in the diamond crystal in order to create a beautifully refractive gem from the raw material.
Graphite, a pure carbon crystal like diamond, is so weakly bonded between its layers that the layers slide readily over one another; hence its use as a lubricant.