'Binary fission ("division in half") is a kind of asexual reproduction. It is the most common form of reproduction in prokaryotes such as bacteria. This process occurs in some single-celled Eukaryotes like Amoeba and Paramecium. In binary fission DNA replication and segregation occur simultaneously. 
In binary fission, the fully grown parent cell splits into two halves , producing two new cells. After replicating it's genetic material, the parent cell divides into two equal sized daughter cells. The genetic material is also equally split. The daughter cells are genetically identical (unless a mutation occurs during replication).
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. After division, the new cells grow and the process repeats itself.