Corrosion is nothing but getting rust to that particular metal or other any substance.
when zinc(zn) comes in contact with oxygen(O2) or is exposed to the moist air zinc reacts with oxygen and gets corroded. after corrosion it turns into brownish colour.
EQUATION : Zn + O2 gives rise to 2ZnO.
i.e., when zinc reacts with oxygen it gives rise to zinc oxide.