Like other organisms, fishes need oxygen for survival. They derive this from the oxygen dissolved in water. But, when large amounts of phytoplankton grow in a pond/lake, they tend to take up all the O2 dissolved in water. As a result, the amount of O2 available for fish goes down dramatically and it dies.
This is why the fishes in the lake die when large number of phytoplanktons grow therein. Such a lake is called a dead lake.