The advice may consist of a literal letter (e.g., "To Whom it May Concern: Your shipment of the 10th inst was received in good order; accompanying is our remittance of $52.47 per invoice No 83046") or of a voucher attached to the side or top of the cheque.
Remittance advices are not mandatory, however they are seen as a courtesy because they help the accounts-receivable department to match invoices with payments.
In countries where wire transfer is the predominant payment method, invoices are commonly accompanied by standardized bank transfer order forms (like acceptgiros (in Dutch) (Netherlands) and Überweisungen (in German) (Germany) which include a field into which the invoice or client number can be encoded, usually in a computer-readable way.
The payer fills in his account details and hands the form to a clerk at, or mails it to, his bank, which will then transfer the money.
Modern remittance advices can include dozens, or hundreds of invoice numbers, and other information.