A chargeback is a reversal of a card payment, made by the customer's card issuer after the customer disputes the charge with their bank.
Chargebacks are run under the card schemes' rules, not by your shop. The customer raises a dispute with their bank, the money is taken back from your payment provider, and you get a chance to send evidence such as proof of delivery, tracking, product photos and your messages with the customer. The bank then decides. Most providers also charge a fee per dispute.
UK credit card buyers have an extra route. Under Section 75 of the Consumer Credit Act 1974, the card provider is jointly liable with the seller for purchases over £100 and up to £30,000, so a customer can claim from the card company if the goods are faulty or not delivered.
The cheapest chargeback is the one that never happens. Fast, clear replies about late or faulty orders give customers less reason to go to their bank. If one does arrive, a calm reply helps, see the chargeback dispute template. This is a general guide, not legal advice.