Cheques likely evolved from bills of exchange, which were used extensively in trade in Venice and Florence, Italy, starting in the 12th century. These city states were at the crossroads of trade with the Middle East, North Africa, the Indian subcontinent and the Far East. Bills of exchange were payable after a certain period—useful for international trade where time delays had to be considered in travel. Cheques, in contrast, were payable immediately, which was better for use in domestic or local transactions.
Why are they called cheques? The word comes from the game of chess, which in French is échec and refers to the action of putting the king in check. The theory is that cheques helped prevent forgeries because they were attached to stubs (actually called counterfoils) in a cheque book. When writing a cheque, the issuer would enter the details of the cheque on the stub. When the cheque was presented for payment, it was matched with the stub and validated. Then the cheque was cancelled and paid out. Over centuries, cheques became a convenient means of payment in private transactions.