Meiosis is the dividing of cells, but not to another full cell with 46 chromosomes. Rather, it creates a sex cell with 23.
Sperm cell meets egg cell. The Sperm and egg are the two sex cells that potentially can be made form Meiosis. The egg is produced during development for females, while males produce sperm throughout their lives.
The process of Meiosis begins with a normal stage of Mitosis. All stages, from the Interstage to the Prophase to the Telophase, happen once. However, after Telophase I, things branch off.
After Telophase I, the cycle of Mitosis is almost completed again. However, the interstage from G1 to G2 is missing. The chromosomes are not duplicated. Thus, when Telophase II occurs, each cell has only half the chromosomes.
A Chiasma is a site where the two different genes in a sex cell may combine or "rub off on each other." The genes exchange information, and thus each gene is changed by its partner.