A term used fairly frequently in the late 18th and early 19th centuries to denote exercises in figured-bass playing, not so much as accompaniments to a solo instrument as self-contained pieces. Composers using this term were very often Neapolitan or Milanese, though the significance of this is unknown. The word may or may not refer to the 17th century practice of divisions, i.e. performing variations on a repeating (figured) bass; more likely it reflects the common Italian practice c 1700 of writing bass lines for keyboard players to work into fully-fledged pieces. (Oxford Music Online)

Robert Gjerdingen is a leading writer in the field of Partimento, with his book Music in the Galant Style.

The home page of the web site containing many many examples