As in "money laundering," a term for the practice of covering up the origins of specific amounts of money. In order to mask the stolen nature of goods and cash, they are repeatedly passed around among specific accounts or middlemen until once again useable untraceably in the common market.
Weapon laundering works in a similar fashion, serving to remove the ID registry from the weapon, rendering it a "non-ID gun" able to be used by anyone.
Colonel Volgin's family had been responsible for the money laundering of the Philosophers' Legacy, making him privy to its whereabouts. When the Philosophers disbanded, he claimed their massive fund for himself.