In the historically familiar bank run during the era before deposit insurance, retail depositors who heard rumors about the health of their bank – whether true or untrue – would line up to withdraw their funds.
If the run continued, then, absent intervention by the central bank or some other provider of liquidity, the bank would run out of the cash necessary to pay off depositors and then fail as a result. Often, the panic would spread as other banks with similar characteristics to, or having a financial relationship with, the one that had failed came under suspicion.