The first reproductive phase of meiosis is prophase; the cell's existence prior to prophase where it was not reproducing is known as interphase. During interphase, the chromosomes in the cell were contained in an organelle known as the nucleus; during prophase, the nucleus dissolves, and the chromosomes become visible. Fibers from the chromosomes extend to the poles of the cell and cross to form a spindle.
During metaphase, the spindle aligns so that the chromosomes are in the middle of the cell. The chromosomes are paired opposite to one another; this is necessary in order to ensure that each daughter cell gets the same amount of chromosomes, though the actual pairing is random.
Anaphase occurs when the paired chromosomes separate from one another and move to opposite sides of the cell. The chromosomes were physically paired by kinetochores, which are a type of protein; it is the motion of kinetochores and the connecting spindles that cause the chromosomes to move.
During telophase, a membrane surrounds each set of chromosomes, effectively condensing them into a nucleus. All of the fibers and spindles dissolve, and cytokinesis occurs. Cytokinesis happens when a protein in animal cells, called actin, splits the cell into two, providing each daughter cell with an identical amount of chromosomes. In plant cells, cytokinesis is not caused by actin but is instead caused by the cell wall.
At this point, two identical daughter cells have been created from one parent cell. If it were to stop here, it would be mitosis. However, sperm cells undergo meiosis, which involves the daughter cells going through all four steps of mitosis again. The important difference is that during the metaphase step of meiosis, identical pairs of chromosomes are not splitting, but rather the individual chromosomes themselves; this results in daughter cells that have half as many chromosomes as their parent cells. Besides metaphase, the stages of meiosis are nearly identical to mitosis. It is important that meiosis creates cells with half the number of chromosomes during spermatogenesis because of the nature of sexual reproduction: those cells are intended to join a female sex cell (also with half the number of chromosomes) to create a new organism.