What was the term when the depositors decide to withdraw their money at once from a savings institution?

The term that you are looking for is "bank run" or "run on
a bank."  This is the term for what happens when a large number of depositors all try to
take their money out of a given bank at once.  This is a problem if so many depositors
try to take money out that the bank runs out of cash to give
them.

Banks do not simply keep all their deposits in a
vault.  Instead, they loan the funds out and only keep small amounts of liquid cash
around.  They rely on the idea that people are not all going to want their money at
once.  But if all the people do want their money at once, the banks are in trouble. 
This is what happened at the start of the Great Depression.  People worried that their
banks would fail so they started runs on the banks.  These bank runs ended up making
many banks fail in the early 1930s.