Copper undergoes a process much like rusting. When exposed to air for extended periods of time, copper oxidizes in a way similar to how iron forms rust. When copper oxidizes, certain chemical reactions form a light green layer over the copper.
Oxidization is the process that has given the Statue of Liberty its distinctive green color, which is known as a patina. Oxidization is also the reason the roofs of many older buildings are green. In addition to changing copper's color, the patina creates a protective, waterproof layer over it, which helps to keep the metal underneath from being further damaged by the elements.