It is a mitzva to have two festive meals on Yom Tov, one by night and one by day. This is one of the primary expressions of the sanctity of the holiday. All the holidays are referred to in the Torah as mikra’ei kodesh (sacred occasions). As the same term is used for Shabbat, in this area the holidays are equal to Shabbat. The Sages elaborate: “How does one sanctify them? With food, drink, and clean clothing” (Sifra, Emor 12:4). Similarly, Rambam writes: “Just as we are commanded to honor Shabbat and enjoy it, so are we commanded regarding the holidays, as the verse states: ‘[Call Shabbat “delight,”] the Lord’s holy [day] “honored”’ (Yeshayahu 58:13). All the holidays [as well as Shabbat] are referred to as mikra’ei kodesh” (MT 6:16; see also SA 529:1).
There is a difference, however. On Shabbat, the Sages ordained, based on allusions in verses (Shabbat 117b), that we partake of three meals, on account of the special holiness of Shabbat. In contrast, on Yom Tov the mitzva is limited to two meals, one by day and one by night (Rosh; Tur). People need to eat two meals every day, and the mitzva on holidays is to turn these meals into notable, festive ones (SA 529:1; Birkei Yosef ad loc. 3; MB ad loc. 13; Kaf Ha-ḥayim ad loc. 24).
It is a mitzva to eat bread at each of these meals (see 2:5 below), and it is a mitzva to have two loaves, just as we do on Shabbat, and for the same reason: since the manna did not fall on Shabbat or Yom Tov, a double portion of manna fell on the day before Shabbat and holidays (SA 529:1; Peninei Halakha: Shabbat 7:3).
Even though Shabbat is holier than Yom Tov, on Yom Tov there is a mitzva to serve better food and wear fancier clothes than those of Shabbat, because of the special mitzva to enjoy Yom Tov, as we will explain in the next section.
It seems from Rambam that on Yom Tov one must have three meals (MT, Laws of Shabbat 30:9, although Beit Yosef suggests it does not necessarily mean this). In practice, almost all poskim are of the opinion of that on Yom Tov there is a mitzva to have only two meals. Tur states that this was the practice of Rosh. This is also the ruling of SA 529:1; Tosfot Yom Tov; SAH; and MB ad loc. 12. Levush explains that because of the extra mitzva of simḥa on Yom Tov, the Sages were not strict in requiring a third meal, as sometimes it is a burden. Ḥida writes that based on kabbalistic teachings, three meals serve no purpose on Yom Tov. Some advise adding a dish to the Yom Tov meal, which can be considered the third meal (one of the opinions in Kol Bo, as cited in MA and MB ad loc. 12). If one gets hungry toward the end of Yom Tov, it seems proper that he eat a third meal or at least have a snack, because otherwise he will suffer on the holiday.
According to most poskim, it is a mitzva to eat bread at each meal, whether because of oneg Yom Tov (Me’iri; Maḥzor Vitri; Responsa Rabbi Akiva Eger §1), or because of the mitzva of simḥa (Ri; Rosh). However, according to Tosafot (Sukka 27a s.v. “i ba’i)” and Rashba, there is no mitzva to eat bread or matza at Yom Tov meals, apart from the first night of Pesaḥ and the first night of Sukkot. See below 2:6, and in the Harḥavot here, regarding one who forgot to say Ya’aleh Ve-yavo in Birkat Ha-mazon.