Deposit insurance is an insurance program that insures peoples' bank deposits in case of bank failure or a run on the bank (or, commonly, both). The biggest deposit insurer in the U.S. is the Federal Deposit Insurance Corp. (FDIC), which is a U.S. government corporation.
Advantages to Individuals
The biggest advantage of deposit insurance to individuals is the peace of mind in knowing that their deposits are not going to become inaccessible if their bank becomes illiquid or insolvent. This means that people are more inclined to put money into their bank rather into other investments or under their bed.
It also helps people on a society-wide basis. If more people put money into the bank, then the bank has more funds to access. This means it has more funds to lend, which in turn lowers interest rates. So, if a private individual wants to get a loan to build an addition on his kitchen, he has the FDIC to thank (at least in part) for his low-interest loan.
Advantages to Banks
Banks, like all businesses, cannot function without an influx of cash. They get this cash from people lending them money at low interest rates in the form of savings and checking accounts. If people lost faith in banks, they would put their money elsewhere, buying commodities, investing in property or simply hanging onto cash. This would render banks insolvent and they would go out of business.
Banks also benefit from the protection that deposit insurance offers. If they make too many bad investments, or leverage themselves too much and end up failing, they do not necessarily go bankrupt. Instead, the FDIC will take them over and put them under new management. Leaders lose control of their bank, but they do not go completely bankrupt as they might without deposit insurance.
When the FDIC assumes control of failed banks, it protects the consumer as well. The FDIC will pay up to $250,000 out of its own budget to each depositor. However, this does not mean that depositors will automatically lose anything beyond $250,000.
When a bank fails, the FDIC's first move is transfer ownership to a bank that is more financially solvent and able to take on the failed bank's debts. If this is impossible, then the FDIC sells off the failed bank's assets to whoever will pay for them, in an attempt to recover enough to allow all depositors to be paid the full value of their accounts. Finally, if this does not work, the FDIC will pay up to $250,000 to each depositor out of its own budget, then attempt to make up shortfalls out of the sale of the failed bank's assets.
The $250,000 figure is how much the FDIC is prepared to spend on each depositor, but it can usually regain their assets without spending this much. The first option listed above—yielding control of failed banks to solvent banks—is effective in the majority of cases.