Did you ever notice that on erev Pesach (the day before Passover), you have to stop eating chometz (leaven) and burn what’s left something like 10:00 or 11:00 in the morning? Sure, you did! But do you know why? The answer is right here, folks!
The korban Pesach (Passover sacrifice) was offered the afternoon before the Seder—that is, the day before Pesach starts. And yet, the Torah tells us to rid ourselves of chometz prior to offering this sacrifice. So, we may no longer have chometz in our possession when the time to offer the korban Pesach rolls around. Eating it after the sixth hour of the day on erev Pesach would be a violation of this mitzvah (see Talmud Pesachim 4b). By rabbinic enactment, one may not even do so during that sixth hour, as a preventive measure. (For more on this, see Rashi on Pesachim 5a, s.v. Chalak.)
The reason for this mitzvah is that eating (or even possessing) chometz on Pesach is a serious matter. Being rid of it far before the holiday begins helps keep us from a sin that could result in a penalty of kareis (spiritual excision). The Torah itself has a built-in fence around this mitzvah, which is extremely important, commemorating as it does the Exodus from Egypt and the miracles God wrought for us at that time.
This mitzvah applies in all times and places. It is discussed in the Talmud in tractate Pesachim (28a-b) and is codified in the Mishneh Torah in the first chapter of Hilchos Chometz u’Matzah. This mitzvah is #199 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #104 of the 194 negative mitzvos that can be observed today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim. The Ramban (Nachmanides) agrees that one may not eat chometz after the sixth hour on the day before Passover but he does not count this among the 613 mitzvos.