A bank run is when all the customers of a commercial bank rush to withdraw their deposits out of fears that the bank might become insolvent. Rumours about a bank's possible collapse may lead to a bank run.
The customers rush to withdraw their money
because they think the bank will be unable to pay them if they wait. But most banks do not have all the money deposited by their customers. They only keep part of it in their vaults as reserves. So a bank might be unable to pay them due to lack of accessible reserves.
When all customers decide to withdraw their deposits at once, the bank becomes insolvent.