As we read in the previous mitzvah, the korban Pesach was slaughtered on the afternoon of 14 Nisan. Since the Jewish day starts at nightfall, when it was eaten that night, it was 15 Nisan, the first day of Passover. Eating the korban Pesach is part of our commemoration of the Exodus from Egypt.
The Rambam explains that eating the korban Pesach with matzah and maror (bitter herbs) is a single mitzvah. He tells us that eating matzah is a separate mitzvah in and of itself (as we shall see), but that maror is only incidental to the korban Pesach. (The fact that we eat maror at our Seders is a rabbinic enactment, as per Pesachim 120a.)
As we mentioned in the previous mitzvah, we use a piece of matzah called the afikomen to symbolize the korban Pesach at our Seders. The korban Pesach was eaten until one was full; the afikomen is eaten on a full stomach. The korban Pesach was the last thing eaten; the afikomen is the last thing we eat. (If anything, the name afikomen is something of a misnomer. The word means “dessert” and the Talmud in Pesachim 119b tells us that it is what we may NOT eat after the korban Pesach.)
Korech, the sandwich of matzah and maror that we eat at the Seder, is a reminder of Temple times. Hillel would very literally eat his korban Pesach in a sandwich with matzah and maror rather just in a meal with them.
The mitzvah to eat the korban Pesach applied to both men and women at the time when the Temple stood. The details of this mitzvah include how much to eat and by when it must be eaten. This mitzvah is discussed in the Talmudic tractates of Brachos (9a), Zevachim (57b) and Pesachim (40b) and in the Mishneh Torah in Hilchos Korban Pesach. This mitzvah is #56 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.