Based on a Naaleh.com shiur by Rabbi Shimon Isaacson
The Torah refers to the matzah as lechem oni (the bread of affliction). The Gemara explains that it is lechem she’onim alav dvarim harbeh, bread over which we say many things. Accordingly, Rabbenu Chananel notes that we recite the hagadah over the matzah. Just as on Shabbat we say kiddush on a cupof wine in order to lend formality and significance to the words, the matzot add an aura of importance to the telling of the story of the exodus.
At the seder there are many foods and props we use to help us get into the mindset of re-experiencing the exile of Egypt. It’s not enough to retell the story. We have to feel as if we are living through it. We taste the bitterness of the maror dipped in brick mortar-like charoset, point to the shank bone symbolizing the korban pesach, and drink the wine of freedom. The matzot too help us remember how our forefathers rushed out of Egypt and how the dough did not have time to rise.
While the word oni in lechom oni is pronounced oni, the ktiv is ayin nun yud, which spells ani, a pauper. Just like a poor person cannot always afford a whole loaf of bread, we take the matzah and break it in two.
In hilchot chametz u’matzah, the Rambam rules that we do not make a blessing on two whole matzot as we usually do on yom tov because the law of lechem oni overrides lechem mishna. In practice, we do not follow this opinion. One matzah is broken at yachatz, and the two other complete matzot are used for motzi matzah.