The term "special prosecutor" first came into use in the United States during the Teapot Dome scandals of 1920s, when Calvin Coolidge appointed outside lawyers to look into the corrupt land-leasing practices of federal officials. Special prosecutors were given more official status in the aftermath of Watergate, when Richard Nixon finagled the firing of the one assigned to investigate him. The Ethics in Government Act of 1978 called for the position of "special prosecutor" to be separate from the executive and legislative branches and to be appointed by a three-member panel of judges from the U.S. Court of Appeals. The act also gave special prosecutors the power to issue subpoenas, start grand jury proceedings, hire a staff, use the resources of the Department of Justice and FBI, and get a security clearance if needed. (Later, the name "special prosecutor" would be officially changed to "independent counsel.")
The Supreme Court upheld the law governing special prosecutors in 1988, but Congress let it expire in 1999 in the wake of Kenneth Starr and the Clinton investigation. In its place, the Department of Justice created regulations allowing for the selection of a "special counsel" on those occasions when there's a conflict of interest within the department. (Patrick Fitzgerald, who led the Northern Illinois U.S. attorney's office, was appointed under those regulations to investigate the Valerie Plame affair.) Unlike the independent counsels that came before, a special counsel serves at the pleasure of the attorney general's office, so he doesn't enjoy the same strict separation from the executive branch.
As for prosecutor Nora Dannehy, she will be a "special attorney."
A "special prosecutor" is an outside lawyer brought in to investigate a government official accused of wrongdoing. He or she isn't directly accountable to the people or agency under investigation, avoiding the potential conflict of interest that a regular prosecutor would have. But Dannehy comes from within the Department of Justice and will report directly to the attorney general and his deputy: Technically, she's a "special attorney," rather than a special prosecutor. That means she was appointed under a section of the U.S. code that allows the government to assign department lawyers to cases outside their home district. Dannehy lives in Connecticut but will be acting under the power of the U.S. attorney for the District of Columbia.