Wiktionary
bank cheque
n. (context banking English) A cheque which is payable by a bank itself, as opposed to an ordinary cheque payable only out of the funds of a particular customer's account. A bank cheque is normally obtained by a bank customer (by paying its face value), the point is that the person receiving the cheque has the security of knowing it's payable by the bank and thus cannot bounce (not so long as the bank is solvent).