Binary fission consists of division of the nucleus followed by the division of the cytoplasm producing two daughter cells each having a nucleus. For example, binary fission occurs in amoeba.
In multiple fission, the nucleus of the parent cell undergoes repeated divisions to produce many daughter nuclei. The cytoplasm also divides and cleaves around each nucleus forming several daughter cells in the parent cell. In favourable conditions when the parent cell membrane ruptures, all the daughter individuals are released. For example, multiple fission occurs in plasmodium.