Cleavage occurs when a mineral breaks along planes of weakness. These weaknesses are a part of the mineral's crystalline structure. Cleavage may occur in one, two, three or all directions.
Many types of cleavage exists. Basal cleavage occurs in minerals that can be peeled off in sheets. Mica exhibits basal cleavage. Small cubes break off in cubic cleavage. Octrahedral cleavage is exhibited when wedges peel off a mineral.
Minerals that fracture have chipped, uneven breaks in the rock. Some minerals that exhibit cleavage can fracture if chipped a certain way. It's possible to identify minerals by examining areas of stress for cleavage and fracture.