The galvanised article is protected against rusting even if the zinc coating is broken. Why and how?

A galvanized substance is that which has been coated with a layer of zinc to delay corrosion.It does this by the zinc getting corroded itself,instead of the substance.
The outer layer of zinc of any galvanized material, reacts with the atmospheric oxygen to form Zinc Oxide (ZnO), which is stronger than Zinc. Thus, even if the outer layer of zinc undergoes corrosion, the material is getting coated with a stronger substance (ZnO), and thus is better able to resist corrosion.