The Torah commands in the book of Shemot, "Ach Ba’yom Ha’rishon Tashbitu Se’or Mi’batechem" – "but you shall eliminate leaven from your home on the first day." The Gemara explains that the "first day" mentioned in this verse refers to the 14th of Nissan, Ereb Pesach, and we are commanded to "eliminate" Hametz from our possession on this day. The word "Ach" ("but"), the Gemara explains, indicates that this requirement applies in the middle of the day. And thus according to Torah law, one must eliminate all Hametz from his possession by midday of Ereb Pesach. However, the Sages enacted as a safeguard that one must eliminate the Hametz already earlier in the day.
What exactly does the Torah requirement of "Tashbitu" – "eliminating" Hametz – entail? How is this fulfilled?
Targum Onkelos translates the word "Tashbitu" as "Tebatelun," which means "nullify." According to Torah law, then, one fulfills the Misva of "Tashbitu" through "Bittul" – pronouncing that he disavows all ownership over Hametz, and that he regards any Hametz in his possession as though it is the dust of the earth.
However, most Rishonim maintain that there is also another way of fulfilling the Torah obligation of "Tashbitu" – by searching through our homes for Hametz and then disposing of it. After all, if simply renouncing ownership over our Hametz suffices, then certainly the physical elimination of Hametz should satisfy the Torah obligation of "Tashbitu." This is the view of the Ran (Rabbenu Nissim of Gerona, Spain, 1320-1380), who writes that even if one does not pronounce "Bittul," he fulfills the Torah obligation through "Bedika" – by searching his home to the best of his ability and eliminating whatever Hametz he finds. Even if it turns out that there was some Hametz in the home which he did not find, he nevertheless fulfilled the Torah obligation because he searched thoroughly, to the best of his ability. This is also the opinion of several other Rishonim (the Ritba and the Maharam Halawa, and of the Rambam, as understood by the Aruch Ha’shulhan). This is the view accepted by the Mishna Berura (331:1) – that one fulfills the Torah obligation of "Tashbitu" through either "Bittul" or "Bedika."
However, the Sages enacted that even if one makes the "Bittul" declaration on Ereb Pesah, he must also perform "Bedika," searching his home the previous night for Hametz, and eliminating all the Hametz he finds. One reason for this enactment is that the Sages were afraid that one’s "Bittul" proclamation might not fully sincere. In order to do a proper "Bittul," one might wholeheartedly and unequivocally renounce his ownership over his Hametz, without any hesitation, disavowing all interest in the Hametz. If someone is anything less than completely sincere in renouncing his ownership over his Hametz, he will not fulfill the Torah’s command, and the Sages therefore required one to also search for and eliminate the Hametz in his home. Tosafot (commentaries by Medieval Ashkenazic Talmudists) add another reason, explaining that the Sages feared that one might find some Hametz in his home during Pesach and eat it. Since we are accustomed to eating Hametz throughout the year, the Sages were concerned that if one encountered Hametz during Pesach, he might mistakenly eat it. The Sages therefore required not only renouncing one’s ownership over his Hametz, but also actually ridding one’s property of Hametz.
In any event, regardless of the reason, we both search our homes for Hametz, and also make the "Bittul" proclamation.
Summary: On the level of Torah law, it suffices for one to simply renounce his ownership over his Hametz on Ereb Pesah, but the Sages enacted that we must also search our homes for Hametz the night before and eliminate all the Hametz that we find, and so we both eliminate our Hametz we find and pronounce "Bittul Hametz" on Ereb Pesach.
