Offline Transaction Processing

Offline Transaction Processing, also known as a signature debit transaction, is a payment method that uses a debit card to transfer funds from a checking account to a merchant across a digital credit cardnetwork. 

When you pay for goods or services with your debit card, you have the option to process your payment in one of two ways:  as an offline transaction via a credit card processing network, or as an online transaction via an electronic funds transfer (EFT) system. Offline transactions are processed much like credit card transactions. They are sent over one of the major credit card networks -- Visa, MasterCard, Discover, etc -- depending on which credit card network your bank is associated with as a member bank. The cost of the transaction, called an "interchange fee," is typically 2-3% of the total purchase

 

(Via Investing Answers)