Chargeback refers to the process which allows consumers to challenge and claw back payments made from their debit and credit card accounts when things go wrong (eg goods or services paid for are not delivered).
Rather than being a legal right, chargeback forms part of card scheme rules (ie set out by Visa, Mastercard, Amex etc) to which the card issuer is a party. A consumer who wishes to dispute a transaction must contact their card issuer to make a chargeback claim.
It should be noted that chargeback is separate to consumer protections under Section 75 of the Consumer Credit Act 1974 which only relate to credit card purchases over £100. For further information read The Consumer Credit Act.