A ledger-to-ledger bank transfer is an old term for transferring money between bank accounts or account books, as stated by AccountingTools. A ledger was a physical book containing a record of all financial transactions for an account.
Modern day bank accounts are sometimes referred to as having a "ledger balance," explains AccountingTools. The ledger balance is the total balance of money in the bank account at the beginning of each day. This total changes depending on the activity in the account.
When a customer initiates a bank transfer, he is sending money from one bank account to another bank account, usually electronically. Bank transfers can also take place between different customer accounts at the same bank.