Card verification code is Mastercard's term, often shortened to CVC, for the security code that the industry more generally calls the card verification value (CVV); that entry explains the code in full.
The code is usually three digits printed on the back of the card, or four digits on the front for American Express, where it is called the card identification number. Merchants ask for it in card-not-present payments to show that the customer probably has the physical card, rather than just a stolen card number. The issuer checks the value during authorisation. A related value is stored in the magnetic stripe, and chip cards generate dynamic codes instead, so the printed code is mainly an online check.
Different brands use different names, such as CVC2 for Mastercard and CVV2 for Visa, but they serve the same purpose. Under the PCI DSS, the code is treated as sensitive authentication data and may not be stored after authorisation, even if encrypted.