When we acknowledge the coming of Shabbat by saying at the conclusion of evening prayers, "Vayechulu hashamayim v'ha'aretz — And the heavens and earth were completed" - quoting from Parashat Bereishit - we are making a statement about the spiritual state of creation.

...before the first Shabbat...every creature existed for itself.

Shem miShmuel says that before the first Shabbat, the seventh day of creation, every creature existed for itself. Every plant, mineral and animal was an individual without connection to the others. But, with the entrance of Shabbat, a new spirit of life permeated the universe, and every creature became a part of an organic whole, contributing in its own way to the functioning of the universe. Just as when a body is healthy, all the limbs and organs work together in a coordinated fashion, so the universe is meant to work best when all creations play their role in the "organization."

That's the meaning, says Shem miShmuel, of the word Vayechulu (generally translated as "and were completed"). The root of this word (kaf-lamed) is also the root of the word clal, meaning "general principle," and of keli, meaning "vessel." In all instances, unity and coordination is implied. A general principle includes everything, every creature. The purpose of a vessel is to unity all that is within it. The universe became a vessel on Shabbat, and absorbed the general principle of unity. That is why we say Vayechulu on Shabbat.

We achieve serenity...on Shabbat, when our heart and mind work together.

There's a principle in the inner dimensions (the secret level) of Torah that whatever takes place in the spiritual realms applies to the dimensions of space (the universe), time and soul. If Shabbat brings unity and cooperation to the universe, it does so for the soul as well. The heavens and earth in the dimension of space correspond to the mind and heart in the soul/person. We achieve serenity (in Hebrew yishuv hada'at – literally: a 'settled mind") on Shabbat, when our heart and mind work together. When the thoughts sway the heart, and the heart willingly follows the mind, the result is yishuv hada'at. When the mind and heart work together, it leads to a "settled mind." Just as Shabbat brings peace to the universe by uniting creatures, it brings inner peace to human beings, allowing our mind and heart to work in synchrony.

Now we can understand a curious statement by the Ari z'l, who said that Adam's sin was that he did not wait until Shabbat, the seventh day, to be with his wife. Shem miShmuel explains that by not waiting, Adam missed the wholeness and holiness that Shabbat brings, and therefore brought upon himself and Eve the knowledge of good and bad – of separation – rather than the awareness of unity and synchrony that comes with Shabbat.

This first letter of the alphabet, which...represents unity and cooperation, is missing from golah.

We can also now understand the statement of the Maharal of Prague, that the difference between exile (golah) and redemption (geulah) lies in one letter – aleph. This first letter of the alphabet, which has the numerical value of one, and represents unity and cooperation, is missing from golah. Since Shabbat brings the spirit of unity to the universe, it brings geulah – redemption – as well.

[From "Inner Lights from Jerusalem!" based on the Shem miShmuel and other Chassidic and Kabalistic Sources, translated and presented by Rabbi David Sterne]