THE OBLIGATION TO EAT MEALS
The Mishna (Shabbos 117b) states that in case a fire breaks out on Shabbos, it is permitted to save "food for three meals". In this context, the Gemara cites a baraisa (a Mishna-era Tannaic teaching) which debates "How many meals must a person eat on Shabbos?" The first opinion rules three meals, while Rebi Chidka rules four. Rebi Yochanan then explains that both opinions are derived from the Torah (Shemos 16:25). The Poskim rule in accordance with the first opinion that three meals are required on Shabbos.
Despite this obligation being deduced from a Passuk, the Rambam (Shabbos 30:9) seems to imply that the obligation of eating three Shabbos meals fulfills a rabbinic, rather than Torah law. In a similar vein, some argue that the obligation is rabbinic and that the scriptural derivation is only an 'Asmachta' - a support to the rabbinical law (Peri Megadim Mishbetzos Zahav 291:1). However, many opinions rule that it is indeed a biblical law (Levush OC 291, Taz OC 678:1 and others).
ARE WOMEN OBLIGATED?
Despite eating meals on Shabbos being a time-bound commandment, women are also obligated to eat three meals on Shabbos. Rabbenu Tam (cited by Ramban, Shabbos 117b) writes that this is because 'they too were involved in the miracle' - referring to the miracle of the Mann as explained below. The Ran (Shabbos 44a), however, argues that this explanation is superfluous since women are equally obligated in all matters pertaining to Shabbos regardless. This is derived from the analogy between the positive and negative Shabbos commandments of 'Zachor' and 'Shamor' (Gemara Berachos 20b).
WHEN TO HAVE THE THREE MEALS?
The Rambam (Shabbos 30:9) rules that “one is obligated to eat three meals on Shabbos—one at night, one in the morning, and one in the afternoon”. This is the clear majority ruling, as ruled by the Shulchan Aruch (291:2). One should therefore be sure to eat the third Shabbos meal in the afternoon (from a half-hour after Chatzos - halachic midday).
Interestingly, the Halachos Gedolos mentions an ancient custom of splitting the Shabbos morning meal into two, thereby eating two of the three Shabbos meals in one meal. However, other Rishonim dispute this custom, and rule that splitting the morning meal is ineffective. Tosafos (Shabbos 118a) notes the Mishnah implies that the time for eating the third Shabbos meal is from the time of Mincha onwards. In addition to this, they write that splitting the meal in two will cause an unnecessary blessing, which is yet another reason to defer the custom (see also Or Zarua, Shabbos 52).
LECHEM MISHNEH (TWO BREADS) ON SHABBOS AND YOM TOV
The Torah (Shemot 16:22) records that in the desert two portions of Mann fell on Fridays and none on Shabbos (see Rashi Ibid). Based on this, the Gemara (Shabbos 117b) writes that we are obligated to use 'Lechem Mishneh' - 'Two loaves of bread' for our meals on Shabbos. This is brought as halacha in the Shulchan Aruch (Orach Chaim 274:1).
There is a debate here too (albeit this time amongst the Acharonim) as to whether this is a biblical or rabbinical obligation. The Magen Avraham (618:10) indicates that it is only a rabbinic obligation, whereas the Aruch Hashulchan (Orach Chaim 274:1) states that it is a Torah obligation.
It is worth noting that the obligations to use two loaves and to have three meals are mutually exclusive, meaning that if one does not have whole loaves of bread (or Matzah) they should at least use sliced bread to fulfill the obligation of having the meal (Mishna Berura 291:20). See below regarding if one is full at the time of Seuda Sehlishis.
There is also a requirement of lechem mishneh on Yom Tov (Ritva Shabbos 117b, Orchot Chayim Hilchot Yom Tov 2, the Rif Ibid, and Shulchan Aruch OC 529:1). This is because the Mann also didn't fall on Yom Tov (Mishna Berura 529:10 from the Rif).
WHAT SHOULD THE MEALS INCLUDE?
Last week, we wrote about the mitzvah to eat meat and drink wine on Yom Tov. As this obligation stems from the requirement to be happy on Yom Tov, it does not apply on Shabbos (Yabia Omer 4:26,2). However, there is an obligation of 'Oneg Shabbos' - to enjoy Shabbos, which is derived from the Passuk in Yeshayahu (58:13) "וקראת לשבת עונג" - "You should call Shabbos a delight". Some Rishonim say this Mitzvah is biblical (Mishna Berurah 242:1 from Ramban on Emor) while others label it a rabbinical requirement (Sefer HaChinuch 297, Rambam Hilchos Shabbos 30:1,9, Beis Yosef Siman 487).
Therefore, as eating meat and drinking wine are considered festive and enjoyable, the Poskim rule that one should increase in eating meat and drinking wine, as their financial means allow (Rambam Shabbos 30:10, Shulchan Aruch OC 250:2, and Remah YD 341:1 as explained in Shach Y.D. 341:7). However, in contrast to Yom Tov, meat and wine on Shabbos is not specifically mandated and one can also fulfill their households expectation of a festive and enjoyable meal by serving other prestigious and delectable food and drink (Mishna Berurah 242:1).
HOT FOOD ON SHABBOS
It is a mitzvah to prepare hot food in advance for consumption on Shabbos, as this is in the spirit of honor and enjoyment of Shabbos. In fact, one who forbids eating hot food on Shabbos may be suspected of being a heretic (Remah OC 257:8 from the Ba'al Hama'or). See the Mishna Berrura (257:49) who stresses the importance of having hot food on Shabbos.
Obviously, all food must be prepared and left on heat sources in accordance with Halacha. See here for an overview of the laws of heating foods and liquids on Shabbos.
IS BREAD REQUIRED AT SEUDA SHELISHIS?
Being one of the required three meals, is it essential that one try and wash for bread for Seuda Shelishis (the third meal). The Shulchan Aruch (OC 291:1) stresses the importance of the third meal saying "One should be very careful with Seuda Shelishis and writes that even if one is satiated he can fulfill it with [bread] in the amount of an egg. If he cannot eat at all, he is not obligated to cause himself distress. A wise person looks ahead and won't fill up his stomach in the morning meal in order to leave space for Seuda Shelishis". He later explains (291:5) that one is required to have bread "unless he is extremely satiated" in which case one may use other foods.
One should also use two loaves of bread for Seuda Shelishis (Shulchan Aruch 291:4). The Remah (Ibid) rules similarly but quotes a custom that some had to use just one complete loaf.
Opinions vary regarding which foods may suffice in the absence of bread (or Matzah), therefore one should look to eat the following foods in this order of precedence;
Mezonos, like cake and cookies
Savory foods like meat and chicken, which could accompany bread
Non-savory foods like fruits and candy
It is important to note that once our sages enacted the obligation of eating three meals for the purpose of Oneg Shabbos (enjoying Shabbos), fulfilling this obligation is no longer dependent on our own discretion or whether we deem it to be an enjoyment. Rather, it is our duty to work to fulfill this mitzvah, even when it may not be easy (such as on short winter Shabbos days).
KIDDUSH/WINE AT SEUDA SHELISHIS
Unlike the first two meals, there is no requirement to begin Seuda Sehlishis with a cup of wine or to drink wine during the meal (Shulchan Aruch 291:4 from the Rosh and multiple others).
The Rambam (Shabbos 30:10) however, writes that wine should be drunk during Seuda Shelishis. Some understand this to mean that Kiddush must be made again (Tur OC 291), while others explain that he merely requires it to establish the meal as important (Beis Yosef Ibid).
In practice, we follow the Shulchan Aruch who rules that there is no need to drink wine at Seuda Shelishis. Some are scrupulous and make an effort to drink wine (or grape juice) at the third Shabbos meal to satisfy the position of the Rambam (Mishna Berurah 291:21).