Torah contains 5 books in this order: Genesis, Exodus, Leviticus, Numbers, Deuteronomy. Many quotes below are taken from a traditional Haggadah. The rest are related to it.
What mitzvah is the Haggadah trying to fulfill? Or what questions is the Haggadah trying to answer?
כִּי יִשְׁאָלְךָ בִנְךָ מָחָר לֵאמֹר מָה הָעֵדֹת וְהַחֻקִּים וְהַמִּשְׁפָּטִים אֲשֶׁר צִוָּה יְהוָה אֱלֹהֵינוּ אֶתְכֶם.
When your son asks you in time to come, saying: ‘What is the meaning of the testimonies, and the statutes, and the ordinances, which the LORD our God commanded you?'
וְהָיָה כִּי יֹאמְרוּ אֲלֵיכֶם בְּנֵיכֶם מָה הָעֲבֹדָה הַזֹּאת לָכֶם.
And it shall come to pass, when your children shall say to you: What do you mean by this service?
And you shall tell your son in that day, saying: It is because of that which the LORD did for me when I came forth out of Egypt.
3.5
From the Talmud, Mishnah Pesachim, 116b:3
In Every Generation a man is bound to regard himself as though he personally had gone forth from Egypt, because it is said, and you shall tell your son in that day, saying: it is because of that which the Lord did for me when I came forth out of Egypt.
Then you shall say to your son: ‘We were Pharaoh’s bondmen in Egypt; and the LORD brought us out of Egypt with a mighty hand....'
(ח) וַיּוֹצִאֵנוּ יְהוָה מִמִּצְרַיִם בְּיָד חֲזָקָה וּבִזְרֹעַ נְטוּיָה וּבְמֹרָא גָּדֹל וּבְאֹתוֹת וּבְמֹפְתִים.
(8) And the LORD brought us forth out of Egypt with a mighty hand, and with an outstretched arm, and with great terribleness, and with signs, and with wonders.
5.5
From the Talmud, Mishnah Pesachim, 116a:11-16
The son questions his father. If the son is unintelligent, his father instructs him [to ask]: 'why is this night different from all [other] nights. For on all [other] nights we eat leavened and unleavened bread, whereas on this night [we eat] only unleavened bread; on all other nights we eat all kinds of herbs, on this night bitter herbs; on all other nights we eat meat roast, stewed or boiled, on this night, roast only. On all other nights we dip once, but on this night we dip twice.' And according to the son's intelligence his father instructs him. he commences with shame and concludes with praise; and expounds from 'a wandering Aramean was my father' until he completes the whole section.
(כז) וַאֲמַרְתֶּם זֶבַח פֶּסַח הוּא לַיהוָה אֲשֶׁר פָּסַח עַל בָּתֵּי בְנֵי יִשְׂרָאֵל בְּמִצְרַיִם בְּנָגְפּוֹ אֶת מִצְרַיִם וְאֶת בָּתֵּינוּ הִצִּיל וַיִּקֹּד הָעָם וַיִּשְׁתַּחֲוּוּ.
(27) that you shall say: It is the sacrifice of the LORD’s passover, for that He passed over the houses of the children of Israel in Egypt, when He smote the Egyptians, and delivered our houses.’
11.5
Is this all that we tell our children? No...
(3) And Moses said unto the people: ‘Remember this day, in which you came out from Egypt, out of the house of bondage; for by strength of hand the LORD brought you out from this place; there shall no leavened bread be eaten.
(3) You shall eat no leavened bread with it; seven days shalt thou eat unleavened bread therewith, even the bread of affliction; for in haste did you come out of the land of Egypt; that you may remember the day when you came out of the land of Egypt all the days of your life.
13.5
When do we tell this to our children? Just when they come and ask?
(6) And on the fifteenth day of the same month is the feast of unleavened bread unto the LORD; seven days you shall eat unleavened bread.
(18) The feast of unleavened bread you shall keep. Seven days you shall eat unleavened bread, as I commanded you, at the time appointed in the month Aviv, for in the month Aviv you came out from Egypt.
17.5
In each and every generation, a person is obligated to regard himself as though he actually left Egypt.
To answer their questions, the Rabbis did not just say, "Read the Book of Exodus. Dayenu." No. They created a very complex order of particular excerpts of text to read, discuss, unpack. They created a text that includes their conversations about the text. Through the process of ritually reading these texts and trying to understand their conversation and through adding our own questions and conversation, through following the commands for what to eat and how, some say that we will ourselves come to regard ourselves, through this process, as going through our own exodus.