Binary fission is a method of asexual reproduction used by most prokaryotes (i.e. bacteria). It is a fairly simple process whereby a living cell divides into two equal, or near equal, parts. Asexual reproduction theoretically results in two identical cells. However, bacterial DNA has a relatively high mutation rate. This rapid rate of genetic change is what makes bacteria capable of developing resistance to antibiotics and helps them exploit invasion into a wide range of environments.
Similar to more complex organisms, bacteria also have mechanisms for exchanging genetic material. Although not equivalent to sexual reproduction, the end result is that a bacterium contains a combination of traits from two different parental cells. Three different modes of exchange have thus far been identified in bacteria.
Conjunction involves the direct joining of two bacteria, which allows their circular DNAs to undergo recombination. Bacteria can also undergo transformation by absorbing remnants of DNA from dead bacteria and integrating these fragments into their own DNA. Lastly, bacteria can exchange genetic material through a process called transduction, in which genes are transported into and out of the cell by bacterial viruses, called bacteriophages, or by plasmids, an autonomous self-replicating extra-chromosomal circular DNA.
Binary fission allows bacteria to reproduce incredibly quickly. With the right temperature, nutrients, and fast life cycle, the rate of producing the organism is described as near exponential growth. 
Binary fission happens following the replicated of the genomic DNA. The DNA attaches to the plasma membrane. While the cell elongates, the chromosomes segregate as the plasma membrane pinches inward. When the membrane reaches the middle, the cell starts to split into two daughter cells. This process is called cytokinesis.
Binary fission is splitting a parent cell into two, so daughter cells should be genetically identical. Sometimes the daughter cells could be slightly different from the parent cell, called mutation, by different genetic information. Binary fission occurs rapidly. Rapid rate of genetic change helps to adjust to different environment and allows cells to resist antibiotics. 
- What is a Cell? by the National Center for Biotechnology Information
- Binary Fission International Society for Complexity Information and Design
- Binary fission The Encyclopedia of Astrobiology Astronomy and Spaceflight
- Binary Fission Wikipedia