Approval Response
When you stick your credit card into the chip reading machine, there's that moment when the computer is thinking and you and the sales clerk have to stand there awkwardly, maybe attempting small talk, maybe just sort of shuffling your feet, avoiding eye contact. While you suffer in a micro-social hell, the card reader is waiting for an approval response.
Eventually (hopefully), the machine gets a code verifying that you have enough left on your credit card to make the purchase. That message represents the approval response. (If you don't get the approval, then things get really awkward.)
Once it receives the approval response, the credit card terminal completes the transaction. And you are free to wish the salesperson a good day and escape to the isolation of whatever music is playing in your earbuds.
The term also refers to "I do", just before you step on the wine glass and everyone shouts, "Mazel Tov!"