After replicating its genetic material, the cell divides into two nearly equal sized daughter cells. The genetic material is also equally split. The daughter cells are genetically identical (unless a mutation occurs during replication).
Some biologists use this term for multi-cellular organisms that asexually reproduce by dividing into two (e.g., some starfish). This is also known as 'fragmentation'. Bacteria uses binary fission to reproduce quickly. They have other methods for exchanging DNA with each other.
During binary fission, the DNA molecule divides and forms two DNA molecules. Each molecule moves towards the opposite side of the bacterium. At the same time, the cell membrane divides to form 2 daughter cells. In the process of cell division (in eukaryotes), first the division of nucleus (karyokinesis) takes place after which the division of cytoplasm (cytokinesis) takes place. After division, the new cells will grow and the process repeats itself.