The term 'Bank Robber's Advance Man' refers to a person known as a Caser, which is an acronym for Cashier and Security Expert. This individual is responsible for providing the money and security measures necessary for a successful bank robbery. They are typically hired by the bank robber to provide the necessary funds and security measures to ensure that the robbery is successful. The Caser is also responsible for ensuring that the money is safely transported to the bank robber after the robbery has been completed.