What is the Mystical Significance of the Star of David?

The Zohar (vol. III 73a) states, "There are three knots connecting [three entities] one to another: the Holy One, blessed be He; Torah and Israel." The Jewish soul connects to its Creator through the study and observance of Torah. The triangle represents the connection between these three entities.1

The essence of the soul connects with G‑d's essence through the study of the teachings of KabbalahThese three entities are each comprised of a pnimiyut (inner dimension) and a chitzoniyut (external dimension): The Torah is comprised of both exoteric teachings (the Talmud, Jewish law, etc.) as well as esoteric teachings (the Kabbalah). G‑d's "revealed" energy permeates and provides existence to all worlds, but His essence is completely hidden, transcending all of creation. Similarly, the soul (which is a reflection of G‑d2) has a revealed element, that level that expresses itself within and vivifies the body, as well as an essence that transcends the body.

The double triangle of the Star of David (Magen David) symbolizes the connection of both dimensions of G‑d, Torah and Israel: The external level of the soul connects to the external expression of G‑d via studying the exoteric parts of Torah; the essence of the soul connects with G‑d's essence through the study – and application of – the teachings of Kabbalah.

Another explanation:

Kabbalah teaches that G‑d created the world with seven spiritual building blocks—His seven emotional attributes. Accordingly, the entire creation is a reflection of these seven foundational attributes.

They are: Chesed (Kindness), Gevurah (Severity), Tiferet (Harmony), Netzach (Perseverance), Hod (Splendor), Yesod (Foundation) and Malchut (Royalty).

These attributes are divided into three columns: right, center and left:

Correspondingly, the Star of David contains seven compartments—six peaks protruding from a center.

The upper right wing is Chesed.

The upper left wing is Gevurah.

Correspondingly, the Star contains seven compartments—six peaks protruding from a centerThe upper center peak is Tiferet. Kabbalah teaches that Tiferet finds its source in Ketter, "the Crown," which is infinitely higher than all the divine attributes which are involved in the "mundane" pursuit of creating worlds.

The lower right wing is Netzach.

The lower left wing is Hod.

The center is Yesod. Yesod is "Foundation," and as such all the other attributes are rooted in, and give rise from, this attribute.

The star's bottom that descends from its belly is Malchut—the attribute that absorbs the energies of the higher six attributes and uses them to actually descend and create everything—and "reign" over them.