We clear the ĥametz out of our homes in two ways: in thought and in deed, that is, spiritually and in practice. The removal in thought is done through nullification (bitul) of the ĥametz, declaring it ownerless and considered as mere dust. We do this nullification because we violate the prohibitions of bal yera’eh and bal yimatzei only with ĥametz that belongs to us and that we consider valuable. One who nullifies his ĥametz and considers it to be as dust does not violate any prohibitions on its account. Similarly, if he declares it ownerless, he commits no violation on its account.
In addition to bitul, we also get rid of our ĥametz in fact. The evening of the fourteenth, we search the entire house for ĥametz, and on the day of the fourteenth we eliminate it from our homes.
Although each method independently is sufficient to fulfill the requirements of Torah law, the Sages required that we remove the ĥametz using both methods, to be on the safe side. Thus, we annul the ĥametz orally and physically clear it out of the house.
On the one hand, the Sages did not want to rely on the nullification alone, lest some Jews not annul the ĥametz wholeheartedly and subsequently keep it in their homes to eat after Pesaĥ. Since they had not annulled the ĥametz wholeheartedly, they would violate the prohibitions of bal yera’eh and bal yimatzei by keeping it at home (Rashi, Pesaĥim 2a). Moreover, they were concerned lest, if ĥametz remained in the house, people might eat it by mistake. Therefore they also required removing it from the house physically (Tosafot ad loc.).
Similarly, the Sages did not want to rely on the search alone, lest some Jews not succeed in finding all of the ĥametz in their homes, but then find it on Pesaĥ. In that event, there is a chance that they might wait briefly before burning it – because they would feel badly for a moment about losing their ĥametz – and, in that moment, they would violate the prohibitions of bal yera’eh and bal yimatzei. By nullifying the ĥametz before Pesaĥ, however, they would not violate the prohibitions, even if they hesitated a little before burning the ĥametz (MB 434:6).