It was the custom of the Baal Shem Tov to partake of three meals on the last day of Passover. The third meal, which took place late in the afternoon, was known as the "Festive Meal of Moshiach," or Moshiach's Seuda, for on this day the radiance of Moshiach is openly revealed.
Beginning in the year 5666 (1906) it became customary in Lubavitch for the students of the Lubavitcher yeshiva to eat their Passover meals together in the study hall. That year the Rebbe Rashab joined the students for the third festive meal of the last day of Passover, and directed that each of them be given four cups of wine. The Rebbe has commented that this was obviously intended to become an annual custom.
Moshiach's Seuda was instituted on the eighth day of Passover, as the number eight is connected to the Redemption (being one more than seven -- symbolic of the natural order) and the Haftorah read on the eighth day of Passover contains many of the Messianic prophecies.
One might ask, what is the point of eating an actual, physical meal that relates to the subject of Moshiach?
This festive meal causes the image and the feeling of the future Redemption to penetrate not only all the faculties of a person's soul, including his capacity for action, but his physical body as well -- by means of the physical food that becomes part of his very flesh and blood. Partaking of this festive meal is intended to draw down the radiance of Moshiach into every aspect of one's daily life throughout the year.
This simply means -- as an anticipatory echo of how the world will appear after the Redemption -- that holiness should permeate all of a person's activities, including his physical activities, to the point that he is prepared to sacrifice the innermost core of his soul. This is the yechida within his soul, the element of Moshiach in his soul.
The Rebbe once explained, "The four cups of wine on the Seder night are the cups of Moses our teacher; the four cups of wine at Seudas Moshiach on the last day of Passover are the cups of our righteous Moshiach."
The Baal Shem Tov established a custom to eat a third meal on the last day of Passover. This meal is known as "Moshiach's Meal," for on this day Moshiach's radiance is revealed. This revelation foreshadows the Redemption.
It takes place specifically on the last day of Passover, for this is a day which is added only in the Diaspora. The essence of the added day is that in the Diaspora and in the time of exile, the Jewish people transform 24 mundane hours into a day of holiness. On the last day of Passover this means transforming them into a festival of freedom and redemption. And this process of transformation is the essence of the imminent Redemption - converting the very exile itself into redemption, so that G-dliness is revealed even at the very lowest levels of creation.
The Rebbe Rayatz introduced the custom whereby "Mashiach's dance" takes place during seudas Mashiach.
The Rebbe Shlita has offered two explanations of this name:
(a) This is a dance that is related to the coming of Mashiach and hastens his coming;
(b) This is a dance in which the King Mashiach himself takes part.
From a talk of the Rebbe Shlita on Acharon shel Pesach, 5712