Historically a mandamento was the part of Italian territory under the jurisdiction of a "pretore" which is a kind of magistrate. These divisions were abolished in 1923.
Within Cosa Nostra a mandamento is a district of generally three geographically contiguous Mafia families in Sicily. A capo mandamento representing the mandamento is usually entitled to be part of the provincial Mafia Commission.
References
Mafia Brotherhoods: Organized Crime, Italian Style (2003) Letizia Paoli, Oxford University Press ISBN 978-0-19-515724-6