A normal cheque represents an instruction to transfer a sum of money from the drawer's account to the payee's account. When the payee deposits the cheque into their account, the cheque is verified as genuine (or 'cleared', a process typically taking several days) and the transfer is performed (usually via a clearing house or similar system). Any individual or company operating a current account (or checking account) has authority to draw cheques against the funds stored in that account.
However, it is impossible to predict when the cheque will be deposited after it is drawn. Because the funds represented by a cheque are not transferred until the cheque is deposited and cleared, it is possible the drawer's account may not have sufficient funds to honour the cheque when the transfer finally occurs. This dishonoured or 'bounced' cheque is now worthless and the payee receives no money, which is why cheques are less secure than cash.
By contrast, when an individual requests a banker's draft they must immediately transfer the amount of the draft (plus any applicable fees and charges) from their own account to the bank's account. (An individual without an account at the issuing bank may request a banker's draft and pay for it in cash, subject to applicable anti-money laundering law and the bank's issuing policies.) Because the funds of a banker's draft have already been transferred they are proven to be available; unless the draft is a forgery or the bank issuing the draft goes out of business before the draft is deposited and cleared, the draft will be honoured. Like other types of cheques, a draft must still be cleared and so it will take several days for the funds to become available in the payee's account.