A monopoly is when a company or other entity is completely alone in supplying a particular good or service to the marketplace. Monopolies are usually discouraged in market economies because their dangers are well-recognized. However, in some instances, monopolies are allowed because very high start-up costs would not make competition economically feasible. For example, the supply of utilities can often be a monopoly situation as in the case of water or electricity.
In a market economy, monopolies are able to demand whatever price they want for their product or service because they don't have any competition. Consumers have no choice but to pay the prices demanded, which is especially dangerous if the monopoly supplies a necessity. This means that consumers pay more than what the product or service truly costs -- cost of production and delivery plus a reasonable profit -- and this makes consumers have less disposable income.
When one company controls the supply of a certain good or service to a marketplace, it can also inflate prices by restricting the supply. The company can use the supply of the goods or services as a form of blackmail, withholding supply from the market. This situation is particularly dangerous if a country, for example, is dependent on one supplier from another country to provide a commodity, because the supply will always be unstable since it's dependent on the other country's willingness to sell.
A major disadvantage of having one company supply a certain good or service is that the company has no incentive to provide excellence. The company has no incentive to improve its services or the quality of its goods since people have no choice but to buy what the company offers.
Monopolies are dangerous because they can become immensely powerful and use this power to further benefit themselves and gain even more power. They have the ability to generate vast profits and can use this money to gain political influence. They can also threaten to disrupt or restrict supply and use this for political leverage as well.