The Statue of Liberty is a gift from the French government to the American government given to celebrate the democratic ideals that both countries fought for in the American and French Revolutions. Actually the French helped the Americans to win their war for
independence a lot.
Later the Statue became one of the first things that immigrants would see in the USA when they travelled into the New York Harbour. Immigrants who came by ship were taken to Ellis Island, which is very close to Statan Island, the island which has the Statue of Liberty on it. Thus the Statue of Liberty became the symbol of freedom, democracy and hope which the immigrants were seeking.
Recently there have been a lot of repairs done on the Statue. Originally the statue was brown (It is made of bronze) but with time the medal tarnished and became green.
Of course this is a patriotic and somewhat propagandistic idea of the Statue. What it actually means is for you yourself to decide.
Often people make fun of the Statue of Liberty and draw cartoons showing the Statue falling or being destroyed because they want to show that they are not satisfied with the government and demand a higher standard of human rights than what the US government is acting on.