Transaction capture is another name for payment capture: the step in which a merchant tells its acquirer or payment processor to collect the money for a card payment that the issuer has already authorised. The main entry explains capture timing, fees and how it fits between authorisation and settlement.
The phrase is used in two related ways. In online payments it usually means sending the capture request for an authorised amount, either immediately or later, as in delayed capture when goods are shipped after the order. Merchants can capture less than the authorised amount, known as partial capture, or capture in several pieces. In older terminal-based retail, "transaction capture" can also mean the point-of-sale device recording the transaction data and storing it in the day's batch, ready for submission at the end of the day.
In both cases capture is what turns an approval into a payment that enters clearing. An authorised transaction that is never captured will not be charged, and its hold on the cardholder's funds lapses after the authorisation expires.