The korban Pesach was offered on the 14th day of Nisan, immediately prior to the holiday of Pesach (Passover). All chometz and leavening agents had to be removed before the time at which the sacrifice could be offered. The sacrifice could be offered starting at noon; accordingly, the day is split between “chometz permitted” hours and “chometz prohibited” hours. (See Talmud Pesachim 5a for a full discussion of how this is derived.)
None of the people involved in the preparation of the korban Pesach may still have chometz in their possession – not the one who slaughters it, nor the one who sprinkles the blood, the one who burns the fats, nor any of those who jointly own it (see Talmud Pesachim 63b).
The reason for this mitzvah is that chometz (leaven) is anathema on Passover. The korban Pesach is offered the afternoon before Passover starts, but it would be inappropriate for us to have chometz around as we are involved in this service. In other words, while the korban Pesach is offered before Passover begins, we must be “Passover ready” at the time. Even today, though we no longer have the korban Pesach, we rid ourselves of chometz on the morning on 14 Nisan and go through the rest of the day chometz-free.
This mitzvah applied to both men and women when the Temple was standing. It is found in the Talmud in tractate Pesachim (5a and 63b, as above). It is codified in the Mishneh Torah in the first chapter of Hilchos Korban Pesach. It is #115 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.