This essay discusses understanding mathematics at three levels: 1) Understanding the meaning of terms and notions, 2) Understanding definitions, theorems, and theories by grasping relationships between concepts, and 3) Applying understanding to new situations. Understanding is an indirect process of grasping sense or meaning. The essay also discusses understanding more generally as perceiving relationships between objects of different orders. Understanding involves effort and is characterized by grasping meaning and showing the ability to apply knowledge in new contexts.