A card-present transaction is an individual payment in the category explained under card present (CP), the main entry. It means the card, or a phone or watch carrying a digital version of it, was physically used at the merchant's payment terminal at the time of purchase.
The terminal reads the card by inserting the chip, tapping for a contactless transaction or, less often today, swiping the magnetic stripe. Chip and contactless reads generate a one-time cryptogram that the issuer can verify, and the cardholder may confirm with a PIN, a signature or device biometrics. These checks make card-present payments much safer than online ones, which is why they usually carry lower fraud rates and interchange fees, and why liability for counterfeit fraud depends on whether chip technology was used.
"Card-present transaction" refers to the single payment, while "card present" names the channel. The opposite is the card-not-present transaction. A chip read is covered further under EMV transaction.