There has always been a stong connection between the moon and the menstrual cycle. The moon has its own cycle, growing full from a tiny sliver, and then shrinking back down again. A full cycle the moon (a synodic month) lasts 29 and one half days. The moon's cycle is clear, and very predictable, and it was the first way we measured a month.
Oddly - or perhaps not oddly at all - the human menstrual cycle is very similar to the moon's cycle. The average length of the human menstrual cycle is about 28 days, which is closer to the moon's cycle than any other menstruating animal. Also, women think of the space between their periods as a "month" even though it might not be a calendar month. Some women call their period "the monthlies".
This old association of months, moons and menstruation is even present in our language. Menstruation comes from the Latin word "menses" which means the menstrual flow, but is also the plural form of the word "mensis" which means month. These Latin words for month probably came from the Greek word for moon: mene. The root word "mens" is found in words having to do with measurement - like the word mensuration, which means the act of measuring. The word for the first time a girl menstruates - menarche - is made up of the Greek word for month (men) and the word for beginning (archie). So you can see how closely related are the ideas of measuring time, the moon and menstruation.
In different places at different times all over the world, people have associated the full moon with ovulation and dark of the moon with menstruation. In some places, when the moon dissapears from the sky it was said to be menstruating. Another name for a period is "moontime." Some women still notice that they tend to bleed either at the full of the moon or the dark of the moon, but not at the quarters. Legends of different cultures say that all women used to bleed together, matching their cycles to the cycle of the moon. The moon has always been associated with women. Think of the goddess Diana, the goddess of the moon, and the hunt.
An interesting side note to this is that experiments have shown that
women with irregular menstrual cycles have become more regular by sleeping
with a soft light on in their rooms (to stand in for the light of a full
moon) during the fourteenth, fifteenth and sixteenth days of their cycle,
the days they would ideally be ovulating. After a few months, their cycles
regulate. This is called the Dewan effect, and it seems to show a connection
between light and the menstrual cycle. Perhaps it also explains old traditions
in which women went out and talked to the moon when they were having difficulties
with their periods.