The usual answer is the one given in the Haggadah. The Torah commands us to eat matzah on Pesach in commemoration of the Bnei Yisrael being rushed out of Egypt so quickly that their dough did not have time to rise. It's commonly assumed that this is nothing more than a paraphrase of what the Torah itself says. But why would this make matzah so very important? And is it indeed necessarily what the Torah says?
Fascinatingly, Ramban has a very different approach. According to Ramban (Shemos 12:39), it's not the case that they were too rushed for the dough to rise. Ramban is of the view that even if they would have had time, they would not have waited for the dough to rise and make bread. Instead, Ramban understands the Torah as stating that they had no time to bake the dough into matzos, and instead they had to take the unbaked dough and bake it into matzos along the way. Ramban notes that the Bnei Yisrael had already been commanded to get rid of all chametz as mentioned a few pesukkim earlier (12:19-20), and thus the passuk 12:39 is to be read in light of that, as follows:
And they baked matzah-cakes of the dough which they brought forth out of Egypt, for it was not leavened (due to God's earlier command); (and they could only bake them now) because they were driven out of Egypt, and could not tarry (and bake them earlier)...Ramban is thereby arguing with the Haggadah! One book that I saw claimed that Ramban would never have done such a thing, and must have had a different text of the Haggadah. I don't know that that is necessarily the case; Ramban was not entirely averse to arguing even with Chazal, in certain cases. But, at any rate, we are left with the following question on Ramban's approach - if eating matzah has nothing to do with how the Bnei Yisrael left Egypt but was instead a pre-existing command, what was the reason for it?
(Skip the following small text if you want: One might wish to posit on Ramban's behalf that matzah commemorates the Bnei Yisrael not having time to bake their dough, and that Hashem commanded the consumption of matzah with the foreknowledge of this. After all, it seems unambiguous that the mitzvah of eating matzah has something to do with the haste in which it was baked. This would initially seem to be the meaning of Devarim 16:3:
You shall eat no leavened bread with it; seven days you shall eat matzos, the bread of affliction; for in haste (chipazon) did you come forth out of the land of Egypt; that you may remember the day when you came forth out of the land of Egypt all the days of your life.The usual assumption is that the mention of "haste" is a reference to the pessukim in Shemos 12:33-34 talking about how the Bnei Yisrael rushed out of Egypt without time to see to their dough. But the word chipazon does not appear in these pessukim. Instead, it appears earlier, in Shemos 12:11, before the end of the plagues, with regard to the korban Pesach:
"And thus shall you eat it: with your loins girded, your shoes on your feet, and your staff in your hand; and you shall eat it in haste--it is a Passover to God."And so the notion of eating in haste is not specifically related to matzah. Indeed, Devarim 16:3 is preceded by a passuk commanding about the korban pesach, and it is with regard to this that the Torah continues, "Do not eat ON IT chametz, for seven days eat ON IT matzos, for in haste you left..." - thus, there too the notion of haste is relating to the korban Pesach rather than to matzos. It thus seems that the theme of haste may relate to the general notion of our leaving Egypt in haste, and not to the way in which the matzos were baked.
So, again, we are faced with a question according to Ramban's view: What is the reason for eating matzah on Pesach? Why did Hashem command the Bnei Yisrael not to have chametz?)
Let us first note that this is not the first time we see matzah preceding Pesach. Way back in Bereishis 19:3, Lot serves matzos to the angels. Rashi says it was Pesach, and a very non-rationalist person in a book entitled Seasons of Life claims that "the observance of Pesach is based on the spiritual powers in force at that time of year," and "matzah is representative of certain metaphysical forces in effect at that time." But the idea of Lot observing Pesach and serving matzah to his guests is reminiscent of a certain video about Eisav making a berachah of hamotzi. Is there a more rationalist explanation?
One possible answer is this: Bread, of the chametz variety, is an Egyptian invention.
In Canaan, the lifestyle was a nomadic society of shepherds. The bread that they ate was matzah - not the hard Ashkenazi crackers, but the original, somewhat softer, pita-like matzah. (Which is why Lot served it to his guests.)
Egypt, on the other hand, was a land of farming, which despised the nomadic lifestyle. As Yosef advises his brothers to tell Pharaoh: "You should answer, 'Your servants have tended livestock from our boyhood on, just as our fathers did.' Then you will be allowed to settle in the region of Goshen, for all shepherds are detestable to the Egyptians." The Egyptians had mastered the art of leavening bread, which was unknown to those from Canaan (which may be why Potiphar entrusted everything to Yosef except baking bread - see Bereishis 43:32). Baking leavened bread was of tremendous importance in Egypt - that is why there was a sar ha-ofim, a royal baker. Rameses III has a list containing an amazing variety of breads. But shepherds didn't and don't eat such things - they roam around free, without the burden of heavy ovens and without waiting around for bread to rise.
This would explain why there is an important prohibition against eating leavened bread on Pesach. It is a way of demonstrating that we left Egypt, the land known for its leavened bread, and we became free, like nomads, to travel to the Promised Land.
(This is an adaptation of a post that appeared two years ago. Thanks to David Ohsie for his input. For more on all this, see this article from Neot Kedumim, and also this article and this one. )