I think you are referring to the female human reproductive system. Women are born with all of their eggs already stored in bodily organs called ovaries. After women reach sexual maturity, they will begin to ovulat approximately every 28 days.

Ovulation is when a mature egg that is ready to be fertilized leaves the ovary and travels through another organ called the fallopian tube to the uterus (the womb). If the egg has been fertilized by a man's sperm, then the egg will be an embryo and will attach to the lining of the uterus. Each month, the uterus produces a nourishing lining in preparation for the arrival of an embryo. At this point, the woman is pregnant and the embryo will grow into a fetus and eventually a baby.

Of course, women don't get pregnant every single 28 days when they ovulate because usually the egg is not fertilized. If the egg is not fertilized, then it will not attach to the uterus and the uterus will shed the unneeded lining. The blood and tissue from this shedding exits from the woman's vagina and this is referred to as her period or menstruation cycle.

There's a great video here originally from KidsHealth.org that explains the process that I've described above with an animation.

Depends on the animal. That's the length of the ovulation cycle in humans. For many animals and most plants, this takes a full year.