Super Soul

Rashi: "and rested"
...one regains one’s soul and one’s breath when one rests from the toil of work. Every expression of nofesh/rest is an expression of nefesh/soul, for one regains one’s soul and one’s breath when one rests from the toil of work. He about Whom it is written: "He neither tires nor wearies" (Is. 40:28) and Whose every act is performed by speech [alone, without physical effort], dictated rest in reference to Himself [only] in order to make it understood to the [human] ear with words that it can understand.

BR: "It is a sign forever" (in the previous verse)
Similarly, the initial letters here spell Ohel/ tent, recalling the verse, "You shall know that your tent is at peace (Job 5:24), which the Talmud explains as referring to lighting lamps on Shabbat eve. (Shabbat 34a)

Ramban: "only you shall keep My Shabbats"
Why is the word "Shabbat" plural? According to Kabbalah, He commanded here the keeping of the Shabbats by zachor/remember and shamor/keep, as I have hinted to their secret, this being the reason for the plural My Shabbats. Of these two [zachor and shamor], G‑d says, "for it is a sign" [i.e. He should have said, "for they are a sign"; this shows] that "it" [i.e. the Shabbat] "is the sign between Me and you...that you may know". G‑d says, "You shall keep the Shabbat" and says those who profane it are liable to kareit/cutting off, for "the spirit returns to G‑d who gave it" (Eccl. 12:7), but the soul of one who breaks Shabbat will be cut off.

[B.R.: See Ma'or V'Shamash: it is measure for measure; on Shabbat there is perfect yichud/unity. But he who profanes Shabbat shows he does not believe in that unity and therefore deserves to be cut off from it.]

G‑d states concerning the 7th day that it is "a Shabbat of solemn rest holy to G‑d" (verse 15), because it is the yesod/foundation of the world. It is also "an eternal covenant" (verse 16), and then G‑d repeats that "it is a sign between Me and the children of Israel" (verse 17) meaning that the Shabbat is a sign on the 7th day and the 7th day is a sign and Shabbat is the sign forever. This is also the meaning of "G‑d ceased from work and rested" (verse 17), this being a hint to the "extra Shabbat soul" which comes from the yesod/Foundation of the world, "in Whose hand is the soul of every living thing." (Job 12:10) The learned student in mysticism will understand.

Ohr HaChayim: This verse tells us what we learned (Beitzah 16) that we receive an additional soul on Shabbat, as alluded in the verse "G‑d ceased from work and rested." This rest resulted in an additional life-force soul. This is a profound secret G‑d did not reveal to the nations of the world. The Talmud states that every commandment G‑d gave to the Jewish people He gave publicly in the open, aside from the Shabbat. This is based on the verse "between Me and the children of Israel it is a sign forever." To the question of how could G‑d punish the non-Jewish nations for not having accepted the Torah when He had not told them about the Shabbat, the Talmud responds that all that G‑d withheld from them was that one who observes the Shabbat receives an extra soul on that day.

Remember that it is impossible for man to attain a true likeness of the life that awaits him after death even if we do all in our power to observe Shabbat on earth to the best of our ability. To obtain that kind of life after death, we must first have a semblance of it by means of true Shabbat observance and all that this entails. The additional soul is our key to such attainment of serenity in the hereafter when the time comes for us to leave this world.

Shem Shemuel: "An eternal covenant"
Although Shabbat is just once a week, it is not a temporary interruption of work but borrows from a higher world of eternal rest. The Shabbat is entered into as a tapping-in to a world which has constancy, depth, eternity, wholeness, far from the superficial and alienating parts of conventional life experience.

Zohar Shelach 173:
Come and see: When the Shabbat arrives, the souls come down, to rest on a holy nation. And the souls of the righteous ascend above. When the Shabbat ends, those souls that dwelt upon the children of Israel rise above, and the souls of the just descend.
...what new things in Torah have you heard in that world?
As soon as all the souls that dwelt on Israel have risen above, they rise and stand, in form, in the presence of the sanctified King. The Holy One, blessed be He, asks all of them: what new things in Torah have you heard in that world? Praised is the one that says in His presence a new illumination in the Torah, as so much joy is produced by the Holy One, blessed be He. He gathers His entourage, and says, Hear the new words of Torah, which that soul of so-and-so is recounting. All explain that point in the two Yeshivas, they below, and the Holy One, blessed be He, above seals that item.