Most eukaryotic cells divide and multiply through one of two cellular processes: mitosis or meiosis. The basic premise of both processes is fairly similar: replicated DNA is split and the cell divides to form daughter cells. However, mitosis differs from meiosis in that it produces cells which are genetically identical to the mother cell. Meiosis is typically reserved for and associated with sexual reproduction and is in many ways a more specialised version of mitosis. With that said, mitosis is very important in multicellular organisms for growth, maintenance, and repair of tissue, since tissues require many genetically identical cells to perform the same function. For instance, more bone marrow or muscle tissue is created through mitosis. In humans, all cells, save for cells involved with sexual reproduction, reproduce via mitosis.
Strictly speaking, mitosis occurs near the end of a cell's biological cycle and spans only a very short amount of time compared to the rest of the cell cycle. Each cell can typically undergo its biological cycle about 50 times, though this varies greatly depending on the type of cell. Before mitosis actually occurs, the cell will have already undergone preparations for mitosis, including the replication of all DNA, and gathering more mass for when it divides into two cells. The cell will perform its normal function at all times during this preparation, which is called interphase. However, it ceases cell function during mitosis. Mitosis itself is broken into four general steps: prophase, metaphase, anaphase, and telophase. Some sources will define more steps than these four, but they are generally intermediary sub-phases and can be grouped within the aforementioned four phases.
Prophase: preparing the chromosomes. In prophase, the DNA in the cell nucleus, which normally forms a large indistinguishable mass, begins to condense into distinctly separate packets of DNA, called chromosomes. Since all DNA has already replicated, each chromosome contains two identical copies of DNA. Each copy of DNA is called a chromatid. The membrane of the nucleus begins to dissolve so that the chromosomes may travel out. Tiny microtubules called centrioles migrate to opposite ends of the cell.
Metaphase: aligning chromosomes. Here, the chromosomes align themselves on the equatorial plate, along the center of the cell. The centrioles on the extreme ends of the cell will radiate small protein spindle fibres towards the equatorial plate. Each spindle fibre will attach itself to the centre of a chromatid, so that each chromosome has attached two spindle fibres, each stemming from opposite ends of the cell.
Anaphase: splitting the chromosomes. As you may recall, each chromosome contains a pair of copies of identical DNA. Each chromosome, which is attached to a spindle fibre from opposite ends of the cell, is pulled apart by the fibres into their two identical chromatids. These identical pulled to both ends of the cell by their respective spindle fibres, so that the two new cells will have identical DNA.
Telophase: splitting and reforming the cell. As the chromatids are pulled close to the opposite ends of the cell, they once again decondense back into their normal mass of DNA. The nuclear membrane begins to reform around the DNA, forming two nuclei. As this happens, the spindle fibres also dissolve. In animal cells without cell walls, an actin protein ring of microfilaments forms around the exterior of the cell and contracts, "slicing" the cell into two daughter cells. The cytoplasm is evenly divided amongst the two new cells. In plant cells with cell walls, membrane-bound vesicles form a hard, porous cell plate between the two new cells. This particular process of physically dividing the two new cells is called cytokinesis.
Mitosis is a complex, multi-step process, and different mitotic behaviours are exhibited by many different cells. Some cells, such as neurons, never undergo mitosis at all. Cancer cells, on the other hand, are genetically flawed so that they spent their entire cell cycle in mitosis, repeatedly forming new cancer cells which never perform a bodily function, eventually causing the formation of cysts and tumours. The process of mitosis is widespread and a fundamental concept for anyone doing work in the field of cellular biology.