There is a mitzva to study a great deal of Torah on Shabbat and Yom Tov. As the Sages state: “Shabbat and Yom Tov were given to us solely for the purpose of learning Torah then” (y. Shabbat 15:3).There are three fundamental reasons for this.
First, there is a general mitzva of talmud Torah (Torah study), which the Sages tell us is equal to all the mitzvot (m. Pe’a 1:1; MT, Laws of Torah Study 3:3-9). Every Jewish man is obligated by it, as we read: “Study them and observe them faithfully” (Devarim 5:1). The mitzva to engage in Torah study applies both day and night, as we read: “Let not this book of the Torah cease from your lips, but recite it day and night” (Yehoshua 1:8). Therefore, a person must study Torah all his life. Even on the day of his death, he should try to go to the beit midrash and study Torah (Shabbat 83b). One who stops studying Torah is likely to forget what he has learned. The Torah cautions us about this: “But take utmost care and watch yourselves scrupulously, so that you do not forget…and so it does not fade from your mind as long as you live” (Devarim 4:9; MT, op. cit. 1:3, 10). Anyone who is capable of studying Torah but does not do so is in the category of one who denigrates the word of God (San. 99a). On weekdays, when people are busy making a living, they are limited in how much Torah they can manage to learn, although they are nevertheless obligated to set aside time for Torah both during the day and at night (MT, op. cit. 1:8, 3:13). In contrast, on Shabbat and Yom Tov, when people are off from work, the mitzva of talmud Torah is reinstated in full force. This is why Shabbat and Yom Tov were given to the Jews – so that they could be off from work and able to study Torah. (See Tanna De-vei Eliyahu Rabba §1.)
The second reason is that Shabbat and Yom Tov are holy days given to the Jews to enable them to progress in their Torah study, which will then illuminate the weekdays as well. Shabbat is meant to elevate and illuminate the days of the week, and each festival is meant to shed its particular light on the whole year. Therefore, Moshe instituted that the Torah reading on each festival should be about that particular festival. Additionally, he instituted that people should “enquire and discuss matters pertaining to the day – the laws of Pesaḥ on Pesaḥ, the laws of Shavu’ot on Shavu’ot, and the laws of Sukkot on Sukkot” (Megilla 32a; SHT 429:5). This is also why according to a midrash, God said to Moshe: “Gather together large groups and publicly teach them matters pertaining to the day. Thus, future leaders will learn from you to convene groups every Shabbat and Yom Tov, and assemble in the batei midrash to teach and instruct Israel about what the Torah permits and forbids. Thus My great name will be glorified among My children” (Yalkut Shimoni, Vayak’hel §408). Indeed, delivering derashot (sermons or homilies) of both legal and aggadic nature on Shabbat and holidays has been the practice of Jewish sages throughout the generations. The main drasha, known in Aramaic as “pirka,” would take place by day, and everyone made sure to come and listen to it (Peninei Halakha: Shabbat 5:4 and Harḥavot there). At night as well, on Shabbat and Yom Tov, there would be a drasha. It seems that this was often dedicated to aggada (Mordechai, Pesaḥim §611), and women as well as men would come to hear it (y. Sota 1:4).
The third reason to study Torah on Yom Tov is that it is a fulfillment of the commandment to rejoice on the festival. Torah study makes people happy, as we read: “The precepts of the Lord are just, making the heart delight” (Tehilim 19:9). For the same reason, Torah learning is forbidden on Tisha Be-Av and during times of mourning (Ta’anit 30a; Sha’agat Aryeh §69).
Besides the mitzva to study a lot of Torah during the holidays, there must be words of Torah discussed over the Yom Tov meals, in order to link the food to its spiritual roots. If people gather for a meal but do not share words of Torah, they are considered to have partaken from “offerings to the dead,” because their physical meal has been disconnected from the soul (Avot 3:3; Peninei Halakha: Berakhot 13:8). One must be especially careful about this at Yom Tov meals, for the more significant and enjoyable a meal is, the more it opens people’s hearts and intensifies their feelings. If these emotions are not uplifted with words of Torah and songs praising God, there is a concern that they might turn into lightheadedness and frivolity. For this reason, the Sages condemn the singing of vulgar and inappropriate songs at a meal. If they use verses from Shir Ha-shirim in such songs to do so, this is even more disrespectful:
Our Rabbis taught: If one recites a verse of Shir Ha-shirim and treats it like a song, or recites any verse at a party when it is inappropriate, he brings evil upon the world. The Torah wraps itself in sackcloth and stands before the Holy One, blessed be He, and laments before Him: “Master of the universe! Your children have made me into a harp to play frivolously.” God replies, “My daughter, how else should they keep themselves busy when they are eating and drinking?” To which the Torah retorts, “Master of the universe! If they are students of Tanakh, let them engage in studying the Torah, the Prophets, and the Writings; if they are students of the Mishna, let them engage in Mishna, halakhot, and aggadot; if they are students of the Talmud, let them engage in the laws of Pesaḥ, Shavu’ot, and Sukkot on the respective festivals.” (San. 101a)