Generally speaking, when an enzyme is synthesized at the ribosome in a cell, it is ready to fold and carry out its function. Some enzymes, however, are synthesized in a non-active precursor form, called a zymogen or proenzyme. The zymogen becomes an active protein upon proteolysis at specific sites in the protein. This ends up being a good way to regulate the activity of a particular enzyme, where you keep it in a nonfunctional state until it is needed. Cutting the protein then switches the protein on.

One example is the peptide hormone insulin. Insulin is involved in metabolic regulation. Cells only generate proinsulin, which contains the two active regions of insulin connected by 32 amino acids. The connecting region is digested away by specific proteases, leaving the two functional domains which are connected by two disulfides.

A number of enzymes in the digestive tract also are generated as proenzymes. Some examples include:

zymogen : active enzyme : location

Zymogens also play an important role in the complex cascade of proteins that carry out blood clotting.

Other ways protein regulate their activity:
allostery
modulator protein
isozyme