Black markets involve the buying and selling of goods and services in violation of laws or government mandates.
Silk stockings during World War II and whiskey during Prohibition. People wanted them and the U.S. government said they couldn't have them. Black markets were born to supply the demand ... at a price, of course. In these two examples, the illicit enterprises were not taking business away from legitimate sellers, as silk had been commandeered for war efforts and alcohol had been outlawed.
Nowadays, there are black markets that do cut into the profit of those operating within existing laws. A black market in pirated DVDs, for instance, thrives because people don't want to pay full price. The illegal sellers have lower production costs than the legitimate DVD-producers and are avoiding taxes, so they can sell these copyright-protected items for a lower price.
Black markets can also deal in higher-priced goods, if they are particularly difficult to obtain or very highly desired. Medicines that are in short supply or restricted would fit this description, as would something like ivory, which it is (in most cases) illegal to import into the U.S.
By its definition, there can be black markets in labor as well as goods: employing a nanny or day laborer, for instance, and not reporting that for tax purposes.
Economies with stricter governmental regulation on the flow of commerce tend to have stronger black markets. Some argue that the existence of black markets leads to an increase in related crime.
Communist countries were well known for their practice of supplying limited amounts of consumer goods through state owned stores. But you could often buy popular western merchandise like CDs or Levi's on the black market. Such merchandise was often smuggled into the country, or stolen from or purchased in stores for the priviledged. Similarly, when local currency has an official government exchange rate with hard currencies, you could often buy and sell US dollars or Euros/Deutsche Marks on the black market.