The Statue of Liberty wasn't always green. When it was unveiled in 1886 it was a bright coppery brown, like a new coin.
It is covered in thin sheets of copper, and copper, reacting over the years with the air and the rain, becomes coated in a greenish layer called patina. It took about three decades to change colour completely.
That patina also protects it: which is why it has never been «cleaned» to bring back its original brown.