I assume the name debit card relates to the reduction in the cardholder's checking account balance at the time that the card is used. The checking account balances of a bank's customers are liabilities for the bank. When the cardholder uses his or her debit card, the bank's liability account such as Customer Checking Accounts or Demand Deposits will be reduced. To reduce the normal credit balance in the bank's liability account, a debit entry is required.
The name debit card also helps to distinguish it from a credit card. The use of a credit card means that the bank (or other financial institution) is making a loan or providing credit to the cardholder. Usually the cardholder will receive a monthly statement showing the credit card transactions and must remit at least a portion of the amount owed within a stated amount of time. The bank will also charge interest on the unpaid balances.