Underground banking systems are financial networks that operate outside of normal banking channels to transfer money internationally, avoiding the fees and regulations of conventional banks. Typically used for immigrant workers' transfer of money back to their countries of origin, it can also be used for illegal activities.
Informal funds transfer systems come in a variety of constructs. Some are very old, such as hawalas, which has its origins in the middle ages and pre-dates conventional banks. The informal network of money lenders and businessmen rely on reputations instead of formal contracts. Money is transferred by giving it to one hawala, along with transaction fee, which is generally much less than credit cards or banks charge. In return, the customer is given a code that they can supply the recipient, who takes it to his hawala to receive payment. The money never actually moves but is instead paid through future business deals that generally recoup money by overcharging on invoices.
A modern example of an underground bank is Bitcoin, which is a virtual currency that also avoids conventional bank overhead and fees by not needing them to complete commercial transactions. Bitcoin uses open-source code on peer-to-peer networks to keep a ledger of ownership of every Bitcoin. That ledger is updated constantly world wide to keep a permanent record of every transaction.