Ovaries: Egg and Hormone Production. Ovaries, the female reproductive organs, have two main functions: to produce female germ cells (called eggs or oocytes) and hormones (estrogen and progesterone), which regulate the function of the ovaries.A girl is born with all the germ cells she'll ever have.varies: Egg and Hormone Production. Ovaries, the female reproductive organs, have two main functions: to produce female germ cells (called eggs or oocytes) and hormones (estrogen and progesterone), which regulate the function of the ovaries.