Cell division is the basic process by which
living things grow in size (in the case of
multicellular organisms) or increase in number (in the case of
single-celled organisms).
Cell division in prokaryotes, which are all single-celled, is called binary fission. The result of binary fission is two genetically identical (barring any mutations) daughter cells, which are now independent organisms.
Eukaryotic cells can undergo two different kinds of cell division, mitosis and meiosis.
Mitosis is the standard sort of cell division that occurs in growing, somatic eukaryotic tissues. For example, at the growing tip (apical meristem) of a plant, cells are rapidly dividing by mitosis. The result of a mitotic cell division is two daughter cells, virtually identical (except if any mutations have occurred) to the parent cell that produced them.
Meiosis is a special type of cell division that occurs in reproductive tissues, in the production of gametes (e.g., sperm and egg). The result of meiosis is four daughter cells, each with half the amount of genetic material present in the parent cell. In the typical case, the parent cell is diploid, and the products of meiosis are haploid.