An assistant who you trust with everything

The Mafia boss and his so called right-hand man were arrested by the police

La polizia ha arrestato il capo Mafia e il suo cosiddetto braccio destro

He thought he could make it on his own, but he soon realized that he couldn't possible succeed without the help of his right-hand man

Pensava di potercela fare da solo, ma si è accorto che sarebbe stato impossibile riuscirci senza l'aiuto del suo braccio destro

There are several possible explanations for this expression. One is that the right side of the body is traditionally associated with skill and strength. Another is that it may refer to the soldier who was responsible for the right side of a troop of horses. Besides, in the past, the position on the right of the leader at political or social gatherings was the place of honor