The korban Pesach must be eaten fully roasted, not cooked in water (boiled, stewed, etc.) or only partially roasted (“na” in Hebrew – more than raw, but not quite ready to eat). The basis of this mitzvah is the continuing commemoration of the miracles of the Exodus. The Sefer HaChinuch tells us that roasting is the manner in which royalty ate their meat; the poor were more likely to boil it. By eating the korban Pesach roasted, we are acknowledging the way God elevated us from slavery to a holy nation. (The Chinuch also explains why, according to the Rambam’s principles, eating the korban Pesach cooked or under-roasted would constitute a single prohibition rather than two separate commands.)
Because the korban Pesach was eaten roasted, we very specifically do not eat roast meat at our Passover Seders nowadays. (This is the practice of Ashkenazic Jews, at least.) The reason for this is so that it should not appear that we are trying to fulfill the mitzvah of the korban Pesach in the absence of the Temple. One of the Four Questions asked at the Seder, as described in Talmud Pesachim 116a, used to be “Why on this night do we only eat roasted meat?” After the Temple was destroyed, it was replaced with the question about reclining, but in our day we might as well ask why we DON’T eat roasted meat at the Seder!
This mitzvah was incumbent upon both men and women in the time of the Temple. It is discussed in the Talmudic tractate of Pesachim on page 41a and in the Mishneh Torah in Hilchos Korban Pesach. It is #125 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.