Most mitzvot in the Torah are presented without a reason why, and Hakhel - the mitzvah to gather the entire people together once every seven years during Sukkot following the Shemitah year to hear selections of the book of Deuteronomy - is no exception. There are some who have proposed ideas over the centuries.
The Torah states:
(י) וַיְצַ֥ו מֹשֶׁ֖ה אוֹתָ֣ם לֵאמֹ֑ר מִקֵּ֣ץ ׀ שֶׁ֣בַע שָׁנִ֗ים בְּמֹעֵ֛ד שְׁנַ֥ת הַשְּׁמִטָּ֖ה בְּחַ֥ג הַסֻּכּֽוֹת׃ (יא) בְּב֣וֹא כׇל־יִשְׂרָאֵ֗ל לֵֽרָאוֹת֙ אֶת־פְּנֵי֙ יְהֹוָ֣ה אֱלֹהֶ֔יךָ בַּמָּק֖וֹם אֲשֶׁ֣ר יִבְחָ֑ר תִּקְרָ֞א אֶת־הַתּוֹרָ֥ה הַזֹּ֛את נֶ֥גֶד כׇּל־יִשְׂרָאֵ֖ל בְּאׇזְנֵיהֶֽם׃ (יב) הַקְהֵ֣ל אֶת־הָעָ֗ם הָֽאֲנָשִׁ֤ים וְהַנָּשִׁים֙ וְהַטַּ֔ף וְגֵרְךָ֖ אֲשֶׁ֣ר בִּשְׁעָרֶ֑יךָ לְמַ֨עַן יִשְׁמְע֜וּ וּלְמַ֣עַן יִלְמְד֗וּ וְיָֽרְאוּ֙ אֶת־יְהֹוָ֣ה אֱלֹהֵיכֶ֔ם וְשָֽׁמְר֣וּ לַעֲשׂ֔וֹת אֶת־כׇּל־דִּבְרֵ֖י הַתּוֹרָ֥ה הַזֹּֽאת׃ (יג) וּבְנֵיהֶ֞ם אֲשֶׁ֣ר לֹא־יָדְע֗וּ יִשְׁמְעוּ֙ וְלָ֣מְד֔וּ לְיִרְאָ֖ה אֶת־יְהֹוָ֣ה אֱלֹהֵיכֶ֑ם כׇּל־הַיָּמִ֗ים אֲשֶׁ֨ר אַתֶּ֤ם חַיִּים֙ עַל־הָ֣אֲדָמָ֔ה אֲשֶׁ֨ר אַתֶּ֜ם עֹבְרִ֧ים אֶת־הַיַּרְדֵּ֛ן שָׁ֖מָּה לְרִשְׁתָּֽהּ׃ {פ}
(10) And Moses instructed them as follows: Every seventh year, the year set for remission, at the Feast of Booths, (11) when all Israel comes to appear before your God יהוה in the place that [God] will choose, you shall read this Teaching aloud in the presence of all Israel. (12) Gather the people—men, women, children, and the strangers in your communities—that they may hear and so learn to revere your God יהוה and to observe faithfully every word of this Teaching. (13) Their children, too, who have not had the experience, shall hear and learn to revere your God יהוה as long as they live in the land that you are about to cross the Jordan to possess.
This passage tells us when Hakhel happened, who participated, what happened there, and something that might be understood as addressing why. But what does the Torah actually mean when it says that those "who do not know will hear and learn to be in awe of Hashem your God?"
For Rambam, it would seem that the content of the selections to be read at Hakhel give the people insight into an intellectual relationship with Judaism.
(א) מִצְוַת עֲשֵׂה לְהַקְהִיל כָּל יִשְׂרָאֵל אֲנָשִׁים וְנָשִׁים וְטַף בְּכָל מוֹצָאֵי שְׁמִטָּה בַּעֲלוֹתָם לָרֶגֶל וְלִקְרוֹת בְּאָזְנֵיהֶם מִן הַתּוֹרָה פָּרָשִׁיּוֹת שֶׁהֵן מְזָרְזוֹת אוֹתָן בְּמִצְוֹת וּמְחַזְּקוֹת יְדֵיהֶם בְּדַת הָאֱמֶת. שֶׁנֶּאֱמַר (דברים לא י) "מִקֵּץ שֶׁבַע שָׁנִים בְּמֹעֵד שְׁנַת הַשְּׁמִטָּה בְּחַג הַסֻּכּוֹת" (דברים לא יא) "בְּבוֹא כָל יִשְׂרָאֵל לֵרָאוֹת" וְגוֹ' (דברים לא יב) "הַקְהֵל אֶת הָעָם הָאֲנָשִׁים וְהַנָּשִׁים וְהַטַּף וְגֵרְךָ אֲשֶׁר בִּשְׁעָרֶיךָ" וְגוֹ':
(1) It is a biblical positive command to assemble all Israelites, men, women, and children, after the close of every sabbatical year, when they go up to make the pilgrimage, and recite to them sections from the Torah which will urge them to perform the precepts and encourage them to cling to the true religion, as it is written: "At the end of every seven years, the year set for remission, at the festival of Sukkoth, when all Israel comes to appear before the Lord … gather the people, men, women, and children, and the strangers within your towns…" (Deuteronomy 31:10-12).
Rambam does not define exactly what he means by "the true religion." However, it seems that he understands Hakhel to be an occasion in which the people will be inspired to be more observant of the laws in the Torah.
A generation later, the philosopher Rabbi Levi ben Gershon, the Ralbag, proposes a different reason:
(א) ויצו משה אותם לאמר מקץ שבע שנים במועד שנת השמטה בחג הסוכות. צוה לקרא את התורה הזאת באזני העם האנשים והנשים והטף וגרי הצדק אשר עמהם כדי שיתחנכו כלם לעבודת הש"י ולא תשכח התורה מישראל ואמר כל הימים אשר אתם חיים על האדמה להורות על נצחיות התורה:
And Moses instructed them as follows: Every seventh year, the year set for remission, at the Feast of Booths - He commanded to recite "this Torah" in this ears of the people - men, women, children, and converts, in order to educate everyone to serve the Holy Blessed One and so the Torah is not forgotten from the Jewish people, saying that 'all of the days that you are on the land teach about the eternal nature of the Torah.'
While it seems Ralbag does not disagree with Rambam that there is an element to Hakhel that inspires people in their observance of the mitzvot, he is focusing on a different aspect of what that accomplishes. Rather than just being about observing the laws more intently, Ralbag sees Hakhel as a practice in continuity. By gathering the people every seven years, the "eternal nature of the Torah" will be understood by the people and that will ensure "the Torah is not forgotten from the Jewish people." While this includes observance of the mitzvot, it is an educational imperative for Ralbag as opposed to a religious ideal like it is for Rambam.
The anonymous 13th century text Sefer HaChinukh understands Hakhel through its communal nature. From this point of view, the reason we do Hakhel is to remind ourselves of what makes the Jewish people unique in the world - the relationship to the Torah.
(ב) משרשי המצוה. לפי שכל עקרן של עם ישראל, היא התורה, ובה יפרדו מכל אומה ולשון להיות זוכין לחיי עד, תענוג נצחי שאין למעלה הימנו בנבראים, על כן בהיות כל עקרן בה ראוי שיקהלו הכל יחד בזמן אחד מן הזמנים לשמוע דבריה, ולהיות הקול יוצא בתוך כל העם, אנשים ונשים וטף לאמר מה הקבוץ הרב הזה שנתקבצנו יחד כולנו? ותהיה התשובה, לשמוע דברי התורה שהיא כל עקרנו והודנו ותפארתנו, ויבואו מתוך כך לספר בגודל שבחה והוד ערכה ויכניסו הכל בלבם חשקה, ועם החשק בה ילמדו לדעת את השם ויזכו לטובה, וישמח השם במעשיו, וכענין שכתוב בפרוש בזאת המצוה ולמען ילמדו ויראו את יהוה.
(2) It is from the roots of the commandment [that it is] because the entire essence of the people of Israel is the Torah; and through it are they separated from every nation and language, to be meritorious for life of the forever - eternal pleasure that is not surpassed by anything among the creatures. Therefore since their entire essence is in it, it is fitting that everyone should gather together at one point in time to hear its words, and for the voice to go out amongst the whole nation - men, women, and infants - to say, "What is the great gathering, that we have all been gathered together?" And the answer would be, "To hear the words of the Torah, which is our entire essence and glory and splendor." And they will come from this to tell of the great praise and the splendor of its value; and its yearning will enter all of their hearts. And with this yearning for it, they will learn to know God and merit good, and 'God will be happy with His creations' - like the matter that is written in explanation of this commandment "and in order that they will learn and fear the Lord."
The Sefer HaChinukh proposes by centering the Torah as "our entire essence," people will naturally want to share that wisdom with others and this is how the people will "learn to revere God."
For the Kli Yakar, a 16th century commentator, to understand what Hakhel is trying to accomplish, we have to look at when we do Hakhel. And his understanding of why we do this is quite different than the other three we've seen here.
(ב) ונראה שכל עיקר צורך הקהל זה היה בעבור התשובה, לפי שאמרו רז"ל (ויק"ר לז) שיום ראשון של חג נקרא ראשון לחשבון עונות, ע"כ הם צריכים לעשות תיכף הכנה אל התשובה והכנה זו היא הקהל זה ... שההקהל יש בו צורך גדול אל התשובה כי ע"י שהם מקוהלים יהיו אגודה אחת ... לפי שדווקא בעשרה ימים שבין ר"ה ליה"כ הקב"ה מקבל תשובת היחיד אבל בכל ימות השנה אין הקב"ה מקבל כי אם תשובת הרבים, (ר"ה יח.) ...
(2) And it appears that the whole essence of this hakhel (assembly) is on account of repentance. As our Rabbis, may their memory be blessed, said (Vayikra Rabba 30:7) that the first day of the Holiday (Sukkot) is called the first [day] of the calculation of iniquities. Therefore they must immediate make preparation towards repentance; and that preparation is is this assembly ... since the assembly is very necessary for repentance. As by their being assembled, they would be one group ... since it is specifically during the ten days between Rosh Hashanah and Yom Kippur that the Holy One, blessed be He, accepts the repentance of an individual. However during all [the rest] of the days of the year, the Holy One, blessed be He, only accepts the repentance of the community (Rosh Hashanah 18a)...
The midrash referenced notes that the Torah refers to the day on which we begin using the Four Species as the “first day” even though it actually begins on the fifteenth day of the month. Clearly the Torah means the first day of the festival, however the midrash understands it to be the beginning of centering our awareness towards making teshuvah - not for the matters past which were addressed just days prior at Yom Kippur, but for the future misdeeds that have not yet been done in the coming year. The Kli Yakar reads this midrash to be teaching us about the difference between personal and collective teshuvah.
... ולמה הזכיר הכתוב ענין זה דווקא בפסוק המדבר מן לקיחת ד' מינים ולמה לא הזכיר זה בפסוק המדבר מישיבת הסוכה, אלא לפי שבלקיחת ד' מינים נרמזו כל ד' כיתות של ישראל שיהיו באגודה אחת ... והוצרך הפסוק ליתן טוב טעם ודעת למה דווקא ביום זה נצטוו לעשות מצוה זו שיש בה הוראה שיהיו כל ישראל אגודה אחת שיכפרו אלו על אלו ... ע"כ צריכין לעשות הכנה אל התשובה והכנה זו היא שיהיו כולם אגודה אחת כמו ד' מינים אלו ...
But why did Scripture mention this matter specifically in the verse that is speaking about the four species; and why did it not mention this in the verse that is speaking about sitting in the sukkah? Rather it is because in the taking of the four species, it hints to all of the four clusters of Jews becoming one group ... And the verse needs to give a good explanation and understanding for why it is specifically on this day that they were commanded to do this commandment that instructs that all of Israel be one group to atone for one another ... Hence they need to make a preparation for repentance; and that preparation is that they should all be one, like these four species...
In thinking about the difference between personal and collective teshuvah, the Kli Yakar references another well known midrash about the lulav and etrog in which each of the four species are likened to different types of relationships that Jewish people have with the Torah. That midrash teaches that we bundle together the four species as a symbol of unifying the people. Kli Yakar is noting the connection between the timing of Hakhel corresponding to the beginning of a new year and new Shemitah cycle, as well as its connection to Sukkot and specifically the symbolism inherent in the ritual act of lulav and etrog. For Kli Yakar, then, the purpose of Hakhel and the importance of what it means to “learn to revere God” is to bring the people into a unified purpose of teshuvah.