Anabolism is the building or creation of new compounds during metabolism. Catabolism is the opposite of anabolism, the breakdown of compounds during metabolism.
A synthesis reaction is when two or more stable compounds are combined to form one molecule. In decomposition reactions a compound is split into two or more stable compounds.
Anabolism and catabolism are frequently discussed in the study of protein nutrition. If you take amino acids and combine them the result is protein. During metabolism a protein that is broken down into its constituent parts yields amino acids.