Authorisation reversal is the British and European spelling of the process covered under payment authorization reversal, which explains in full when reversals are sent, how they are formatted and why the card schemes require them. This page gives a short definition.
When a cardholder pays, the card issuer approves a payment authorisation and usually places a hold on the amount, reducing the available balance or credit line. If the sale is then cancelled, the goods are not shipped, or the final amount turns out to be lower, the merchant or its acquirer should send an authorisation reversal. The reversal tells the issuer to release some or all of the held amount straight away, instead of waiting for the authorisation to expire.
A reversal is different from a refund. A refund returns money after a transaction has been cleared and settled, while a reversal undoes an authorisation that never reached clearing, so no money has actually moved. Card networks set time limits for sending reversals and can charge fees when merchants leave unused authorisations open, because stranded holds annoy cardholders. Reversals are common at hotels, fuel pumps and car hire desks, which often authorise an estimated amount first, may top it up with an incremental authorisation, and then reverse whatever part of the hold the final bill does not use.