Payment authorization is the step in which the payer's bank or card issuer checks a payment request and approves or declines it, usually in a second or two while the customer waits. An approval reserves the funds or available credit but does not move money yet. How authorization fits with clearing and settlement is explained in Authorization & Settlement.
For a card payment the request travels from the merchant through the acquirer and card network to the card issuer, which checks the card status, available balance and fraud signals, and may ask the cardholder to confirm with 3-D Secure. An approved authorization places a temporary hold on the funds. Money changes hands only at settlement, and an authorization that is never captured simply expires. Approval also does not end the merchant's risk: a chargeback can still follow.