it's simple- if ppl feel their savings is in danger of disappearing, they will withdraw their cash from the bank. This could potentially cause what is called a "run" on the bank as everyone takes out their cash in a panic-- then the bank will run out of operating cash and the bank will fail. there are many ppl who have amounts greater than 100-K in savings and they should not have to worry about it being gone. if they feel confident that their savings is safe they'll leave it alone, and the bank can continue to function.
IMO this is very important, because it will encourage depositors leave their cash IN the bank and therby keep individual banking institutions solvent. The last thing we want is more and more banks to fail, especially the "small" community ones.