The bitul ḥametz text is in Aramaic because it was composed when this was the vernacular. Yet one is free to recite it in Hebrew or any other language, as long as he understands what it means. If one utters the declaration in Aramaic without understanding its general significance as an act of bitul, thinking instead that it is an Erev Pesaḥ prayer, he has not nullified his ḥametz (MB 434:9).
The Rishonim explain the significance of the bitul (nullification) in two ways. Rashi and Ramban explain that human beings have the power to nullify ḥametz. This capacity is unique to the context of ḥametz, since according to the Torah ḥametz is entirely insignificant during Pesaḥ. It is forbidden to derive benefit from it, and consequently it is like the dust of the earth. In one respect alone does ḥametz retain significance during Pesaḥ: if it remains in one’s home, he transgresses the law of bal yera’eh and bal yimatzei, but if the owner nullifies his ḥametz before it becomes forbidden, his intention is in accord with the Torah’s intention, so even if ḥametz remains in his possession during Pesaḥ, he will not have violated bal yera’eh and bal yimatzei.
Tosafot explain that the bitul is effective because it renders the ḥametz ownerless (hefker), and the Sages teach that bal yera’eh and bal yimatzei apply only to ḥametz one owns, not to ownerless ḥametz.
Thus, according to the first explanation, the nullification focuses on the ḥametz itself, while according to the second explanation, the nullification is directed at the owner, who relinquishes his ownership over the ḥametz. The Ashkenazic version of the declaration takes both explanations into account, and therefore mentions both nullification and renunciation of ownership. The Sephardic version mentions only nullification, which includes renunciation, for if something is nullified it consequently becomes ownerless.