The Torah tells us that a woman who has a menstrual flow is rendered ritually impure by it for a week; such a woman is called a niddah. As with other forms of ritual impurity, she is able to transmit this form of uncleanliness to others. A person who touched a woman during her niddah period could immerse and be purified at nightfall but if a man had sexual relations with her during this time (which is prohibited, as we shall see), he would be rendered impure for a full week. Even if the woman became purified in the interim, the man would remain impure until his week was up.
This is one of those things that drives some people crazy for no good reason. They perceive that considering a natural bodily function as a source of impurity is backwards and misogynistic. What they fail to recognize is that there are many, many sources of ritual impurity. (One of them, in the previous mitzvah, is the impurity caused by a seminal emission, which is a male thing.) The only reason that niddah impurity is still practiced today is that it has a practical application. While most forms of impurity only prevented a person from entering the Temple or eating from sacrifices, menstrual impurity renders a woman forbidden to her husband. That’s something that makes a difference even in the absence of the Temple, so this particular form of impurity continues today. If we lived in a time where we enjoyed the Temple and sacrifices, no one would hypothesize niddah as “anti-woman” because it would be in the context of many other forms of purity and impurity that would potentially be a part of life.
As far as an underlying rationale for the mitzvah, I speculate the following: The greatest source of impurity is a corpse. The carcasses of certain animals are also possible sources of ritual uncleanliness. What’s a menstrual flow? It’s tissue that’s expelled from the uterus when the woman has not become pregnant. In other words, it’s tissue that had the potential to nurture life but failed to be so transformed. This is not the same as death, but in some aspects it resembles death. (The same can also be said of semen, which also imparts ritual impurity, albeit to a different degree.)
We will speak more about the reasons for niddah impurity, especially in the context of a marital relationship, when we come to Mitzvah #207, the prohibition against engaging in acts of physical intimacy during this time.
This mitzvah applies in all times and places to both men and women. (Men also have to deal with the realities of niddah impurity.) As with other forms of ritual impurity, but it has extremely limited practical application in the absence of the Temple. (Actually, this mitzvah has no real practical application; it’s Mitzvah #207 that we observe today.) This mitzvah is the subject of the Talmudic tractate of Niddah; it is codified in the Shulchan Aruch in Yoreh De’ah 183 and is #99 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.