A bank run is created when customers begin withdrawing their money en masse because they believe the bank will fail (i.e., become insolvent). After customers begin withdrawing their money in a panic, it causes more customers to withdraw money. If enough customers withdraw their money, the bank will default. Basically, the bank runs out of money. The FDIC was established in 1933 as a result of bank runs.
Bank runs are not as common in modern times because many customers know that their deposits are insured by the FDIC. This doesn’t mean a bank run can’t occur. Banks don’t keep all of their customer deposits on-site. For security reasons and regulations from the Federal Reserve, only a small percentage of actual deposits are kept in the bank.