Tammany Hall was the commonly used name for the political machine that ran New York City for a very long time. Its power was at its peak in the mid-to-late 1800s and early 1900s.
Political machines were corrupt organizations whose members used their powers to enrich themselves and to ensure that they would continue to be elected. They used their political power to force businesses to give them money in exchange for contracts and other favors. They used the money to enrich themselves, but also to provide assistance for the voters (many of whom were poor immigrants) who kept them in office. They would ensure loyalty on the part of the voters by giving them jobs and other sorts of assistance. The political machines were a particular target of good government reformers in the Progressive Era.