A bag man (or bagman), is a person designated to collect money in a protection racket, who in this context may also be known as a delivery boy or running man.
Originally the term applied only to Mafia members collecting for mob bosses, but the term later spread to use in corrupt police precincts for patrolmen who picked up and delivered bribes from the local mob(s) to the precinct captain.
The bagman may receive a fraction of the money collected. The term can also be used for a person who performs small tasks for the Mafia, such as chaffeuring, transportation of goods, or even shakedowns.
The term is also used pejoratively to describe fundraisers for political parties and employees of the IRS.
The Oxford Concise Dictionary defines "Bagman" as an "agent who collects or delivers money for illicit purposes".