These are fees paid by one bank to another to cover the handling costs and credit risk in a bank card transaction. Because interchange fees generally flow from the seller toward the bank that funded the transaction, there is some risk assumed by the funding bank in the process.
Consider a credit card transaction - the merchant bank (also called "acquiring bank," as it processes the sales drafts of merchants and pays them together in a lump sum) pays an interchange fee to the bank that issued the credit card. The issuing bank then bills the cardholder. However, the card-issuing bank is now responsible for payment to the merchant bank - and there is no guarantee that the cardholder will make the payment. Meanwhile, when the acquiring bank pays the merchant, it deducts a merchant discount rate - the interchange fee that goes to the issuing bank, plus a profit for the acquiring bank itself.
The interchange fee is a percentage of the transaction amount, and it is derived from an accounting formula that takes into account authorization costs, fraud and credit losses, and the average bank cost of funds.
In ATM and debit card systems, interchange flows in the opposite direction - when a consumer gets cash, the bank that owns the ATM collects the fee.
See also: Credit Card Industry