The Even Ezra explains (Shemos 15:35) that the nes of the mann, which sustained Bnai Yisroel for forty years, was the greatest of all miracles which they experienced in the midbar. Unlike all the other nissim which were isolated occurrences, the mann served as daily testimony affirming Divine providence.
Even today we acknowledge and communicate this nes each Shabbos. The Gemara (Shabbos 117b) explains that the requirement of lechem mishna, having two challos at each Shabbos meal, and the obligation of shalosh seudos, three Shabbos meals, stem from the nes of the mann. Indeed, Rabbeinu Tam explains that although women are generally exempt from time bound positive commandments, they are obligated in lechem mishna and shalosh seudos, based on the principle of af hein hayu b'oso hanes, they too were included in this miracle.
Interestingly, the mitzvah of seudas Shabbos has two different sources. The Torah teaches "Vayomer Moshe ichloohu hayom ki Shabbos hayom la'donay hayom lo timtsaoohu ba'sadeh - Eat it today for today is a Shabbos for Hashem - today you shall not find it in the field" (Shemos 15:24). The Gemara (Shabbos 117b) explains that the word "hayom", today, which is found three times in this passuk, alludes to the three Shabbos meals.
The Gemara (Pesachim 105a), however, brings a second source for seudas Shabbos. Yeshaya Hanavi emphasizes (58:17) "v'karasa laShabbos oneg l'kedosh Hashem mechubad" - if you proclaim the Shabbos a delight, and the holy day of Hashem honored."
These two sources - "ichloohu hayom" and "v'karasa laShabbos oneg" - emphasize different aspects of seudas Shabbos highlighted by several halachic differences. "V'karasa laShabbos oneg" underscores the need to have two meals on Shabbos, one at night and the other during the day (Pesachim 105a). "Ichloohu hayom", however, stresses the requirement of an additional third meal. In fact, the Mechaber (Shulchan Aruch O.C. 529) maintains that whereas the mitzvah of oneg applies even on Yom Tov, "ichloohu hayom" is limited to Shabbos. Therefore, the mechaber asserts that on Yom Tov there is no need for seudas shlishis, an additional third meal.
Furthermore, although oneg requires a complete festive meal which includes pas, bread, the Mechaber (Shulchan Aruch O.C. 291) cites several views regarding "ichloohu hayom". Therefore Mechaber concludes that although one should wash and have challah at seudas shlishis, if one forgot to recite retse v'hachalitseinu in Birkas Hamazon at the seudas shlishishe he is not required to repeat Birkas Hamazon.
The Mechaber further explains that if one was unable to have a Shabbos meal leil Shabbos, Friday night, he should eat three meals during the day. This Halacha can be understood in light of the two sources for seudas Shabbos. One who failed to partake of a seudah on leil Shabbos missed the opportunity to fulfill the mitzvah of oneg balayla. He is nevertheless obligated to have a total of three meals based on the passuk of ichloohu hayom. In such a case, his first meal on Shabbos morning is rooted in the mitzvah of oneg. The next two meals, however, are based on ichloohu hayom.
Accordingly, one can understand the view of Birkei Yosef who maintains that in this case, when one failed to have a seudah on leil Shabbos and therefore has three meals during the day, if one failed to include retse v'hachalitseinu in Birkas Hamazon in the second meal, he need not repeat the Birkas Hamazon. In this instance, the second meal is similar to seudas shlishis, whose basis is the passuk of ichloohu hayom.