Hametz is an allusion to the evil inclination. Concealed within the commandment to search for hametz everywhere, burn it, and nullify it, lies the answer to the question of how one should combat the evil inclination.

It is known with regard to this prohibition, that hametz contains an allusion to the evil inclination. One’s good inclination must overpower his evil inclination…. This alludes to the notion that just as we are commanded by Torah law to nullify the hametz in our hearts, so too, we are obligated to nullify the evil inclination in our hearts so that it does not rule over us. And just as the tradition comes [that is, rabbinic law dictates] to burn the hametz and to search our houses for it in every hole and crack, so too, are we obligated to search deep inside ourselves for evil thoughts. (Rabbeinu Baĥya ibn Ĥalawa, Kad HaKemaĥ, Pesaĥ 1)

Further reading: For more on hametz, what it is, and how to destroy it, see A Concise Guide to Halakha, pp. 274, 286.

Hametz is different from matza in that it rises. As a result, hametz symbolizes pride, whereas matza symbolizes humility and self-abnegation.

Matza reflects the real nature of things, without any inflation of the truth:

As it contains no leaven, matza does not rise, expand, or become thicker or heavier after baking. Rather, it remains the same after baking as it was at the outset, without any expansion. It comprises just the essential elements of flour and water, kneaded together.

By contrast, hametz signifies an inflated image of one’s true essence:

This is not the case with regard to leaven; it expands within the dough, making it rise considerably. The dough appears large and substantial, having expanded and thickened on all sides, and is much larger than it was previously. And it expands in a way that signifies haughtiness, as its height increases gradually [and increased height indicates haughtiness].

The puffed-up hametz symbolizes pride, whereas matza symbolizes self-nullification and humility:

The Jewish people were commanded to eat matza…so that they would possess the attribute of complete self-nullification. (Rabbi Shneur Zalman of Liadi, Siddur Im Derekh Etz Ĥayim, p. 284)

Further reading: For more on humility and pride, see A Concise Guide to the Sages, p. 432.