Originally, in the Western world, coins were pieces of a metal which was worth something in itself (gold, silver) so the value of the coin was dependent on how much metal was in it and could be decreased by clipping the edges off. However, much of Asia tended to make coins out of relatively low-value metals throughout history, and rely on the power of the issuing government to give the coin value, just as they did with paper money. It was the late 20th century before many Western countries abandoned the idea that coins were only worth the value of their weight in metal. But now coins are generally made of materials chosen for durability and availability so that the value is arbitarily set by the issuer of the coin.

Source: Bernstein, Peter L. The Power of Gold: The History of an Obsession. New York: John Wiley & Sons, 2000.