Rabbi Arthur Waskow

On Pesach: three matzot and the Afikomen
The hiding and finding of the Afikomen are defined as part of the "seder" ("order of service") of Pesach by being mentioned in the chant of the structure as "Tzafun," "Hiding." Why? Well, there are several reasons.
The simplest is that we want the dinner to end with the taste of slavery/freedom in our mouths -- thus the taste of matzah, which is both, rather than fruit or macaroons or some other unrelated sweet.
(Check what we say to the wise child -- "There is nothing permitted to be eaten after the Afikomen" -- an originally Greek word, "epikomioi," which means the "after-revels" -- either dessert or drunken reeling from house to house after the"symposium" ["drinking-together"] dinner on which the Seder is modeled. This becomes -- "No after-revels/dessert permitted; end with the Afikomen.")
But the "after-taste" commitment explains eating extra matzah late, not the charade of hiding it etc. This can be explained on either or both of two levels: the earthiest -- it intrigues the kids, like any hide-and-go-seek game -- or the deepest, most mystical: we are affirming the sense of the Hidden and Mysterious in the universe.
AND -- these may be the same thing. That is, kids may love hide-and-seek precisely because it evokes a deep truth of the world. We might fruitfully ask ourselves what the grown-up versions of hide-and-seek are that we play, and whether they meet our deep needs for dancing with Mystery or not.
On this theory, we hide the larger "half" of the broken matzah because we are affirming that there is more that is Hidden, Mysterious, in the world than any information we can gather.
As for the three matzot: One version, Koheyn, Levi, Yisrael. Another (modern): thesis, antithesis, synthesis. (I wouldn't be surprised if Christians think it's the Trinity.)
There is also a Kabbalistic tradition for why three matzot. It is based on the teaching that all the formal Seder objects represent the 10 (and shadowy eleventh) Sphirot or emanations/ aspects/ of God, which are reproduced in the human being because we are "made in the image of God."
According to this teaching, the cover on the matzah is the highest, ineffable Sphirah, Keter ("Crown") which is practically the Eyn Sof, the undiscussable Infinite. The three matzot are Chochma (Intuitive Wisdom), Binah (Discernment, making distinctions), and Da'at (intimate intertwined Knowledge).
In this view, we break the Binah matzah because Binah IS brokenness -- the break in the unitive flow of life and Spirit -- the ability to say Beyn uVeyn, "Either/ Or." Chochma is the Tree of Life, Binah the Tree of Knowing Good & Evil. Eating from that Tree is necessary -- see Eden -- but/and it also leads to brokennesss in our lives. (See Eden!) AND -- from that brokenness and only from that brokenness can we grow into freedom. [That last bit is my own; take it, eat it, with a grain of salt. Of course.]
In the human body, Chochma is the right brain-hemisphere, Binah the left brain, and Da'at either the corpus collosum that connects them or the mouth that expresses them outward to make Knowledge intimately intertwined (practically sexual in overtone).
In another view, we break the middle matzah -- the one from which we then eat, as well as hiding the larger part -- because matzah is the bread of affliction so long as anyone keeps the whole thing for her/himself, and becomes the bread of freedom only when we share it -- with the Hidden One and with each other.
According to this system, the objects on the Seder plate are the next six Sphirot, based according to their physical placement on the plate (upper right is Chesed, etc.), and the plate itself is the seventh/ tenth -- Malkhut, or Majestic Ingathering, the Shekhinah.
And I have suggested that the Orange on the Seder plate provides an aspect of Malkhut that is "figure," visible, where before it has been only "ground," the almost-invisible background.
by Rabbi Arthur Waskow,
Director, The Shalom Center.