What it is:
A bank failure occurs when a regulator closes an insolvent bank. An insolvent bank can't meet its obligations to depositors (e.g., it doesn't have the money to meet withdrawal demands) or to creditors (i.e., it can't pay its debts).
The Federal Reserve, the Federal Deposit Insurance Corporation (FDIC), and the Office of the Comptroller of the Currency have the power to close banks. The National Credit Union Administration has the power to close credit unions. States also regulate banks and credit unions, and those authorities also have the power to close insolvent financial institutions.
How it works/Example:
Let's say Bank ABC has used too much of its deposits to make loans and that many of those loans go into default. As a result, Bank ABC doesn't have the cash to service its withdrawal requirements or pay its own creditors and becomes insolvent.
If that happens, regulators step in and have two roles:
1.) insure the deposits
2.) sell or collect the bank's debts and assets
When a bank fails, the FDIC notifies depositors of the event in writing immediately after the bank closes. In most cases, another bank indicates that it's willing to assume the failed bank's deposits and liabilities, and the FDIC helps arrange the match. Because another bank essentially assumes the balance sheet of the failed bank, borrowers still have to repay their loans -- though likely to a new bank, which becomes the lender.
If the FDIC can't find another bank to assume the assets and liabilities, however, it pays the depositors out of its insurance fund. Typically, if a bank fails, bank customers have access to their money in either case within 24 hours. The money in the FDIC's insurance fund comes from insurance premiums banks have already paid, plus interest earned on the investment of those premiums in U.S. Treasury securities.
The FDIC's standard insurance amount is $250,000 per depositor per insured bank. Deposits in different categories of legal ownership at the same bank may be separately insured, meaning that individuals aren't necessarily capped at $250,000 of coverage. (The FDIC lays that out here).
Why it matters:
Bank failures are rare occurrences, but when they occur they can be very jarring to the economy. The foundation of the banking industry is trust, so when banks fail, people often worry their money held in other banks will disappear too. That's why reassurance is at the heart of the FDIC's mission -- its goal is to protect depositors' money. That's one reason an FDIC-insured bank must display an official FDIC sign at each teller window, according to the FDIC.