Very quickly, money is not actually real but works on trust. ie you trust that if you went to your bank you will get all your money.
In reality, if everyone went to the bank to ask for their money out at the same time, it would cause a ru (ala Its a Wonderful Life). the money is not actually sitting anywhere for everyone to take it out - it is in houses, stocks etc.
It would be impossible for everyone to take their money out of the banks though to pay their debts off as more people have debts than savings.