As noted, the wording of our bitul ĥametz is in Aramaic because it was composed in an era when this was the vernacular. Yet one is free to recite it in Hebrew or any language he understands. If one utters the declaration in Aramaic without understanding its general significance as an act of bitul, thinking instead that it is an Erev Pesaĥ prayer, he has not nullified his ĥametz (MB 434:9).
The Rishonim explain the significance of the bitul (nullification) in two ways. Rashi and Ramban explain that man has the power to nullify ĥametz. This capacity is unique to the context of ĥametz, since according to the Torah ĥametz is entirely insignificant during Pesaĥ. It is forbidden to derive benefit from it, and consequently it is like the dust of the earth, lacking all importance. In one respect alone does ĥametz retain significance during Pesaĥ: if it remains in one’s house, he transgresses the law of bal yera’eh and bal yimatzei. However, if one nullifies his ĥametz before it becomes forbidden, he has fulfilled the intention of the Torah, and if such a person keeps ĥametz in his possession during Pesaĥ, he will not have violated bal yera’eh and bal yimatzei.
Tosafot explain that the bitul is effective because it renders the ĥametz ownerless (hefker), and the Sages teach that bal yera’eh and bal yimatzei apply only to ĥametz one owns, not to ownerless ĥametz.
Thus, according to the first explanation, the nullification focuses on the ĥametz itself, while according to the second explanation, the nullification is directed at the owner, who relinquishes his ownership over the ĥametz.
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.