In the third Seudah of Shabbat it is written: “and I shall feed thee with the soil of Jacob thy father” [Isaiah 58:14]. This is the Seudah of Ze’eir Apin in its fullness. And all the six days are blessed by this fullness. And one has to rejoice in the Seudah and fulfill these meals, that they are meals of fulfilled faith, of the holy seed [“Zar’a Kadisha”] of Israel, of high faith.

We discover here that in the third Seudah we eat “the soil of our father Jacob”, “the seed of Israel”. The Seudah Shlishit is the time in which the commemoration of keneset yisrael (henceforth: Kns”Y), and her ascension to the magnitude of Kise’ D’Arich Anpin, happen. Kns”Y ascends over to the high worlds and communes with itself; and thus the people of Israel also participate in the Godhead and become drawn near to it. We may draw similarities to the Eucharist, in which Jesus, who is, as we know, based on the character of keneset yisrael (Yeshua=Shechina with total), gets eaten and drunk by the believers, and thus communes with them. A massive point of similarity, which can also be seen as a point of distinction, is that the Eucharist makes the communion of the church with Jesus possible, all while the Seudah Shlishit participates in the yichud (or perhaps, in a rather pauline language, “communion”) of Malka Kadisha (the world/totality) with Atika Kadisha (the interior Godhead). In addition, the Eucharist is a medium for the communication of grace and love over to humanity, while the Seudah Shlishit affirms and opens the gates of abundance and arouses the desire (“Ratzon” or “Ra’ava”).
The relations between Kns”Y and KuB”H are intimate and carnal relations, in which there is maintained an unceasing dialogue expressed in the Jewish liturgical calendar. Shabbat is a time in which these relations reach a climax of proximity, as the gates of ratzon are opened and the Godhead turns familiar with itself. In the yichud of sod hashabbat, Israel are communing and rising beneath Elohi”m and become one flesh and one world.
In derush inyan minchat shabbat in sha’ar hakavanot by R’ Chaim Vital, the Seudah Shlishit matter is elaborated upon:

I have already noted to you of the matter of seudat hamincha, that now Atika Kadisha copulates in the aspect of mouth in Him, from and within [“Mineh U’Veh”]. And from the plenitude drawn from this Zivug we eat this Seudah.

Hence, in Seudah Shlishit we eat together with Z”A (thus RaCha”V comments: this is why we call this Seudah “Seudata D’Ze’eir Apin”) and together with Him we are fed with the abundance of Grace springing from the Chochma of Dikna D’Arich Anpin (an abundance which is, apparently, originating in an oral autosexual activity of Atika Kadisha.) In addition the RaCha”V comments that we should not conduct a kiddush on the wine in Seudah Shlishit because the wine is considered a Judgement and in Arich Anpin there is no Judgement, only pure Grace. The transition from Judgement (“din”) to Grace (“Rachamim”) is represented by the name Y”H (representing the attribute of Judgement), which, when filled with alephim (YO”D H”E’, יוד הא), equals HVY”H (as hinting on the ascension of Ze’eir Anpin). This is why instead of doing a kiddush on the wine one needs to do a kavanah for the filling of Y”H with alephim. And so Y”H’s filling transforms during Shabbat from yodim (Shabbat evening) through hehim (Shabbat morning) to alephim (Shabbat mincha).
Hence, in Seudah Shlishit there occur both transubtantiation (the transition of the food from matter onto spiritual seminal waste) and transpotency (change and natural internalization of forces within the Godhead). And so there also occurs a self-sharing of God with man, and so self-sharing of organs in the divinity with other organs. The Seudah becomes a time of interiorization, self-affirmation and gathering of the divinity into itself.
In addition, the Seudah as the celebration of the abundance descending in the hours of ratzon is an expression of the loose love, the pouring-out, the exteriorization and the being-communicated of the divinity to the people of Israel, who also take part in the divine changing, raise the worlds of creation (BY”A) to the world of concept (“atzilut”) and rise to the level of Z”A, where they are free to draw plenitude from the high Holy Partzuf.