1. Bills of exchange.
An acceptance is a bill of exchange which has been 'accepted' by a high quality credit - usually a bank - effectively guaranteeing payment and thereby enhancing the credit quality of the bill.
2. Trade finance.
A trade acceptance.
3. Law - contract.
Acceptance is one of the essential requirements for the formation of a contract under English law.
Another essential requirement being an offer.
4. Payment systems.
Abbreviation for acceptance for settlement.
5. Agreeing to receive.
More broadly, agreeing to receive something.