Shabbat is the Hebrew name for Saturday. Shabbat means rest. G-d commands the Jew to rest on Shabbat from 39 forms of creative labor called “Melachot”, and celebrate the day with prayer, Torah study, formal dress and festive meals.

The Askmoses Answer:

Body

One of the great virtues of the human being is his ability to achieve, to create, to do. Man is unique in this regard and this unique ability is an attraction hard to ignore. It is so attractive that we often get swept away by this one aspect of our being, overlooking other elements of being, namely, being itself; we forget to rest, we forget to be. We are so obsessed with making a living that we forget, neglect, or simply don't have time, to live.

At its very basic, Shabbat is a Divine remedy for that imbalance. It establishes a balance for doing and being, making a living and living.

Shabbat is an oasis in time, an Exodus from the pressures of daily life, a moment to transcend creation and unite with creator.

On Shabbat there is no business or work, deadlines or meetings; only quality time for introspection, meditation, prayer, and festivity. For one day a week your universe precludes clients or bosses. A world emerges in which to discover family, community, G-d and yourself.

This balanced system comes from G-d Himself. G-d created the world in six days and on the seventh day, Shabbat, He rested. I.e. G-d allotted six days for doing, and one day for being. As the Torah¹ says "Six days a week you shall work... and the seventh shall be a day of rest."

G-d created the world in six days and on the seventh day, Shabbat, He rested. I.e. G-d allotted six days for doing, and one day for being.

Soul

Shabbat, however, is not just a break from what we do; it is a portal into who we are, and subsequently adds significance to everything we do.

Shabbat is to the week what the soul is to the body. You might only pay active attention to your soul periodically, but it is constantly vitalizing and inspiring your every moment. Similarly, Shabbat only comes around once a week, but it enhances the performance and perspective of your whole week.

We are reminded that there is more to the creator than His acts of creation; there is a concept of Divine rest, a Divine "soul", an inner existence and not just an outwardly expression. The Torah² writes and "on the Seventh day He ceased and rested". The Hebrew word for rested, "Vayinafash", is actually from the root word Nefesh "soul". I.e. on the Seventh day He [expressed] His soul. He provided a day for us to discover Him rather than His work. 

We are also reminded that there must be an aspect within our own psyche that is beyond the acts of our creation. We realize we possess an inner spirit that needs as much (if not more) attention and development as our external 'matter(s)'.

On Shabbat we have an increased revelation of the soul,³ and this spiritual enhancement has a permanent effect on us and everything we do. The Zohar⁴ says "All the days of the week are blessed from Shabbat".

In Judaism the days of the week don't have names; they are just Yom Rishon - a first day (from/to Shabbat), Yom Sheini - a second day (from/to Shabbat) etc. When Shabbat is over and the next week begins, it is not just another week, but a new week. A new spiritually enhaced you emerges into a new spiritually enhanced world. It is a "first day".

Thus Shabbat not only transcends the mundane; it is the Divine in nature.

See also How is Shabbat celebrated? and Shabbat A-Z.

Suggested reading: And on the seventh day thou shall not rest; Shabbat: Music Between the Notes & Shabbat: The Inside Story.