First for protein being amphoteric, It means that it has the ability to behave as acids or bases,
So the significance of protein being amphoteric in living organisms, is that it contribute to maintain the PH in living organisms that also is very important for the living systems to work clear, changes in PH can have drastic consequences for important cellular molecules such as proteins itself, which in turn can have disastrous effects on the metabolism and structure of the cell; for this reason organisms can exist only in fairly narrow range of PH.