The verse "a three-fold cord is not quickly broken" is interpreted by our Sages to refer to the three Patriarchs--Abraham, Isaac and Jacob--whose lives formed an unbreakable chain that continues to exist to this very day. Chassidut teaches that this three-fold bond alludes as well to the bond of love connecting souls together.
The origin of this cord is the secret of the initial ray of G-d's Infinite light filling all the worlds. This ray of light, which continues to shine and enlighten all existence, is the bond of love between the Creator and His Creation.
The root of the word mitzvah ("commandment"), as explained in the Talmud, is "to connect together." The performance of mitzvot are our attempt to return the ray of light to G-d by connecting ourselves and the world we live in to their Source, ever deepening our connection of love of G-d, Torah and Israel.
The phenomenon of the cord being three-fold reveals multiple layers of meaning. The letter gimel, whose numerical value is three, is shaped like a walking foot, representing, on different levels, the expression of dynamic movement. In relation to angels, who are referred to as "those who stand," men are referred to as "those who walk": "And I shall make you those who walk amongst those who stand" (Zechariah 3:7).
Abraham, Isaac and Jacob represent dynamic response to life's trials and challenges, ever walking forward and upward. The three axis-lines of the sefirot, symbolized by the three Patriarchs, represent the principles of harmony and balance in a world of obvious duality. Herein lies the secret of the Magen David, the star of David, whose form of two intersecting triangles creates an image of symmetry and balance.
The vowel in the Hebrew language associated with the sefirah of chesed, lovingkindness, is the segol, a triangular arrangement of three dots. The word segol appears in one of the most crucial verses in the Torah, in which G-d appoints Israel as His special people: "...you shall be to Me the most beloved treasures [segulah] of all people, for Mine is the entire world" (Exodus 19:5). The word "most beloved treasures" has come to be translated as "the chosen people," a phrase replete with meaning and possible misinterpretation. This alludes to the role of the Jewish people as a pivotal balancing energy between the physical and spiritual worlds, creating a holistic and integrated world-view amidst the apparent duality of existence. It is the third Temple which will be called "a House of Prayer for all people," binding everyone together, as we pray fervently on Rosh HaShanah and Yom Kippur: "Let humanity all become a single society."
Another related manifestation of the three-fold cord is the statement of the Sages: "On three things the world stands: on Torah, on service, and on acts of lovingkindness" (Avot 1:2). These three pillars correspond to the three Patriarchs (Torah to Jacob, service to Isaac, and lovingkindness to Abraham), each blazing a pathway in the foundation of rectifying the world.
Inasmuch as every Jew has all three of these root-souls within him, he can relate on a very deep level with every other Jew. "All of Israel is responsible one for the other" (Shavuot 39a, Sotah 37a, Rosh Hashanah 29a). This level of responsibility is only possible when one fulfills the commandment "and you shall love your fellow Jew as yourself."