Binary fission is used by most prokaryotes for asexual reproduction. This process replicates the original, or mother, cell, to produce two identical daughter cells.
The fission process begins when the DNA of the mother cell is replicated and joins into a circular structure, pair by pair; each circular DNA strand then attaches to the plasma membrane. Near the site of attachment, the cell elongates and causes the two duplicated chromosomes to separate. At this point, the plasma membrane invaginates, or pinches inward toward the middle of the cell; when it reaches the middle, the cell splits into two daughter cells.
Organisms reproducing through binary fission grow in numbers exponentially. Provided that there are adequate nutrients and a reasonably fast life cycle, a single organism can multiply into billions or more relatively quickly.
It is common that one of the resultant daughter cells is not identical to the mother due to the relatively high mutation rate of bacteria. This tendency to change is what makes bacteria develop resistance to antibiotics, and what enables them to rapidly adjust to different environments.
Web Resources On Binary Fission
Cell Division: Binary Fission & Mitosis
Book Resources On Binary Fission
Molecular Biology of the Fission Yeast by Anwar Nasim, et al
Essential Cell Biology: An introducton to the Molecular Biology of the Cell by Alberts & Raff