Human beings are conditioned by their deeds. What we do affects how we feel. Hence the power of the rituals of the Seder: Eating matzah and doing the other rituals to remember the Exodus reinforces our belief in G-d as the Creator, His sovereignty over nature, and His ability to suspend nature at any time, as He did in Egypt.
From the perspective of the inner dimension of Torah, the "soul" of Torah, matzah is more than a symbolic reminder of the Exodus--its very ingestion contains a mystical power to strengthen our faith.
The Talmud teaches that babies don't know to call out "Father" or "Mother" until they "taste the taste of grain."
This alludes to the idea that the food we ingest affects our psyche. In a similar vein, when we eat matzah (which is made of grain), we gain the ability to "recognize" our "parent," our Father in heaven and call out to Him.
Now, babies at that age don't understand how their parents are their parents and why they should love them. They react with an intuitive knowledge, not a rational one.
Our recognition of G-d gained through the matzah is likewise a non-rational one. For it enables us to "know" G-d even as He transcends the limits of our intellect.
Such knowledge is possible only through the humility of faith, which we acquire by ingesting the humble matzah.
"Matzah shemurah is called by two intrinsic and inherent names: Food of Faith and Food of Healing. It strengthens the faculty of daat (internalization)." - The Baal Shem Tov.
"Matzah strengthens the health of the body by helping it perceive the purpose of the soul's descent into the body. Matzah is therefore also the Food of Faith, meaning that it causes the unshakable faith [of the soul] to permeate every aspect of our lives."
- Rabbi Yosef Yitzchak of Lubavitch
Pesach is distinguished from all other holidays, since on Pesach we receive our physical sustenance through a G-dly food. Our lives are uplifted to the loftiest heights during Pesach, and especially on the night of the Seder.