Anabolism is the part of the body's metabolism that is dedicated to building up - specifically the building-up of molecules, muscles, and other tissues from simpler components. The "other half" of metabolism is catabolism, that's the breaking-down part. So that it could be correctly said that a bodybuilder, like the gentleman posing on the right, catabolizes his diet, and spends hours in the gym in order to enhance the anabolism of his musculo-skeletal system.
This division between the metabolic processes of catabolism and anabolism is an artificial separation made by those who study life processes, artificial in the sense that since anabolic activities in metabolism take up energy, they are actually never really totally separated from the other division - catabolism, the processes that supply energy.
In other words, the catabolic (breaking down- energy releasing) steps of our metabolism are always tightly coupled to the anabolic (building up - energy requiring) steps of metabolism.
Like the two faces of a single coin, anabolism and catabolism make up the set of chemical processes that occur in every living thing that are- together- called metabolism.
