In very simple terms, as with any business, if the amount of money they owe to other people exceeds the amount they have, or are due to receive, then they are technically bankrupt. This usually comes to a head when they are unable to pay someone who takes some sort of legal action to recover money they are owed. I don't know what you believe makes a bank different to other types of business, other than the fact that people who have money "in" a major clearing bank have some protection and would not lose their money in the event that it did go bankrupt.