The male and female germ cells are called gametes. The gametes in human males are produced by the testes, two globe-shaped reproductive organs just below the penis. Male gametes are what most people refer to as sperm. Gametes in human females are produced by the ovaries, two oblong organs on each side of the uterus in the lower abdomen. Female gametes are what most people refer to as eggs or ova. After sexual intercourse, an ejaculated sperm cell penetrates an egg and unites with it (fertilizes it). The fertilized egg is called the zygote.
The reproductive organs in both males and females (testes and ovaries, respectively) begin gametogenesis with a primitive germ cell. A primitive germ cell is a seed cell. Like a seed planted in a garden, a primitive germ cell initiates the process that eventually results in a new being. The primitive germ cell contains 46 pairs of chromosomes. Chromosomes are structures that hold the genetic information (the DNA) that determine the makeup of the new being. In humans, chromosomes influence hair, eye and skin color, height, bone structure, and all of the characteristics that prompt people to say that a child "takes after" his mother or father.
Chromosomes occur in pairs because they reflect the makeup of the previous generation -- 23 chromosomes from the father and 23 from the mother. However, the gametes produced by the testes and the ovaries cannot each contain 46 chromosomes. Otherwise, after they unite, they will contain 92 chromosomes. Thus, the germ cells produced by the testes and ovaries each divide once, then divide again, in a reduction process that creates cells containing 23 chromosomes, or half the original number. This reduction process is known as meiosis.
Then, after a male ejaculates sperm into a female and fertilizes her egg, a new individual with 46 chromosomes begins to form. This is the beginning of pregnancy.
"Gamete" is derived from the Greek word "gamete" (wife) and "gamein" (to marry). "Genesis" is derived from the Greek word "genein" (to produce). Thus, in gametogenesis, cells marry ("gamein") and produce ("genein") a new being.