"Monopoly" is a term from economics that refers to a situation where only a single company is providing an irreplaceable good or service. Because the firm in question is the only place where the good or service can be found, they have the ability to charge whatever they want, to the detriment of market competition that is the foundation of a healthy economy. Such a company is said to be monopolizing a portion of the market.
A recent example of a monopoly would be that of the pharmaceutical giant Pfizer over the drug Viagra®, which at the time of its release had no substitutes or competitors. This was a side effect of being the inventor of a product for which there is high demand but no preexisting supply. Other monopolies occur when consolidation across industries results in a single supplier. This was the case with the company Standard Oil, which had to be broken up by the government in 1911.
Some economists argue that the market should be left alone almost entirely by the government, and if monopolies form, that is the will of the market and should not be meddled with. Most economists, however, even those who wish for low government interference in private markets, acknowledge that in some special interests an anti-trust action, such as an anti-monopoly legal ruling, is absolutely necessary.
Accusations of monopoly are common whenever a single company gains a large market share in the supply of a product. A classic example from the last few decades is Microsoft, though their supremacy over operating systems and Internet browsers has been eroded by the open source Firefox browsers and Linux operating systems, respectively, as well as Mac's Safari browser and Mac OS. Microsoft has been engaged in lengthy legal proceedings in the past over accusations of monopoly.
In the 1910s and 1920s, numerous anti-trust laws were drafted and put into action by the US Government, as the adverse effects on the economy produced by them were especially unwelcome during the Great Depression. Examples of present-day monopolies include the NFL with American football, the MLB with American baseball, DeBeers, which controls most of the world's diamond markets, and AT&T, which was broken up in 1982 but has been reconsolidating recently.