The name "Albany Regency" was a disparaging description used by Thurlow Weed to describe the Democratic political machine created in New York state by Martin Van Buren in the 1820s. The machine continued to operate while Van Buren was out of the state serving in the Senate, hence the allusion to a regency, which is government by designated people who rule during a time when the king is not available.
The original name for the group was the "Holy Alliance." Active on both the state and national levels, the Regency was extremely effective in maintaining party discipline, manipulating people through a shrewd use of patronage. While the members were not regarded as personally corrupt, they gained control of party conventions, where they were able to determine nominations and afterwards receive appointments for their friends from the lucky officials. The term "spoils system" can be traced to a statement by William L. Marcy in 1833, to the effect that he could see no wrong in the principle that the spoils belong to the victor.
Eventually this faction split into groups known as the “Barnburners” and the “Hunkers." This division deprived the group of its power of political patronage, and let to the Regency's dispersal after Van Buren's defeat in the 1848 election.