Definition: A monopoly is when a business, usually a large corporation, is the only provider of a good or service. Monopolies are usually bad for an economy because they restrict free trade, which allows the market itself to set prices.
Since monopolies are the only provider, they can set pretty much any price they choose, regardless of demand, because they know the consumer has no choice. They can also supply inferior products. They are also bad for an economy because the manufacturer has no incentive to innovate, and provide "new and improved" products.
Monopolies were made illegal in 1890 by the Sherman Anti-Trust Act. It was called Anti-Trust because that was the form that monopolies held in those days. A group of companies formed a trust to fix prices low enough to drive competitors out of business. Once they had a monopoly on the market, these trusts would raise prices to regain their profit.
Sometimes a monopoly is necessary to ensure consistent delivery of a product or service that has a very high up-front cost. This is true, for example, with electric and water utilities. Since it is so expensive to build new electric plants or dams, it made economic sense to allow a monopoly for a particular area. To protect the consumer, these industries were regulated by the federal and local government. The companies were allowed to set prices to recoup their costs and a reasonable profit. In the 1990's, there was much talk of deregulation to allow competition, and in some cases this in fact occurred.

