Question: Why does the Torah say (See Leviticus 12:1-5) that for a mother to recover from the impurity of birth it takes twice as long for a girl than it does for a boy?
Answer: Rabbi Avraham Ibn Ezra says that this is a reflection of some physiological difference between the formation of a boy in the womb, and a girl. For a girl, it takes the mother’s body longer to clear itself out after the birth, and recover completely.
Rabbi Samson Raphael Hirsch gives a more esoteric reason (and I saw this also in several other commentaries). They say that the doubled time for a female birth is because the time corresponds to the baby plus the mother, since each possess the ability to give birth to life. For a boy the time is for the mother alone. Clearly, both explanations need more work to understand them properly; see how Rabbi Hirsch explains it.
As for the split within each set of times, 7 + 33 etc., the commentary of Rashi explains that the first time period is when the woman is a “nidah”, forbidden to her husband. During the later time period (33 or 66 days), she is called “tehorah”, pure, because she’s permitted to her husband. She is still “t’meiah”, impure, as regards going to the Tabernacle or being able to eat sacrifices.