In the retail payments arena (such as credit and debit cards) authorization refers to the communication between a consumer's bank and the merchant's bank verifying that the consumer has sufficient credit or funds available in their demand deposit account (DDA) to cover the transaction, in which case the consumer's bank (also known as the card-issuing bank) sets aside funds for the transaction and provides the merchant's bank with an authorization code.
Essentially an authorization is the approval or permission to perform specific activities or receive access to specific resources. For example, if you hire a car, an authorization will be obtained for the amount required as a deposit from your credit card.