G‑d "created the world that it might be settled". (Isaiah 45:18) This implies a level of civilized conduct, which can be achieved only when every human being also observe their divine laws.
Indeed, the perfection of the world that leads to the Messianic Era requires the understanding and implementation of the divine laws that G‑d through the Torah provided for all humanity.
In Kabbala and Chassidut, the Seven Divine Laws are equivalent to the seven lower sefirot.
The ten sefirot, through which G‑d made the world and man, are divided into three "intellectual" attributes: Wisdom, Understanding and Knowledge (chochma, bina, and daat), and seven "emotional" ones: Kindness, Might, Beauty, Eternity, Glory, Foundation and Sovereignty (chesed, gevura, tiferet, netzach, hod, yesod and malchut).
The three intellectual attributes are associated with the Jewish people who provide the legal and spiritual interpretations of the Seven Divine Laws to the descendants of Noah. Each law parallels one of the seven "emotional" sefirot.
Sexual misconduct is the perversion of love, and is related to chesed. Sexual transgression disrupts G‑d's love for us and harms people in their love-capacity, while permitted sexual relations are cherished in Heaven, and facilitate divine influence throughout creation.
Murder is the perversion of strength and power, and corresponds to gevura.
Theft is the destruction of harmony in human relationships, and corresponds to tiferet, the harmonious blend of kindness and might which enables social balance. In a world where questions of business morality are at the top of the agenda, this commandment fosters ethical conduct in an area where it is sorely needed.
Idolatry and Blasphemy correspond respectively to netzach and hod, which are often paired together as the two supports of faith. Idolatry is a violation of divine rulership, and blasphemy of divine love. Since G‑d's rulership and His love are inseparable, each in turn facilitating the other, so too these two commandments support and enhance each other. G‑d alone is to be worshipped, directly and without any conjoining or intermediary, and He alone desires and hears prayer out of His love for all mankind.
War comes to the world through the delay of justice…
Eating a limb from a living animal corresponds to the sefira of yesod, associated with the reproductive drive. The link between eating and sexuality is well-known. The eating of living meat fosters the purely rapacious aspect of both eating and sexual relations. It adds to the desire for purely exploitative sexual relations which resemble eating, since such food contains the actual "heat of life" which arouses selfish passions. Sexual rapaciousness and cruelty of all kinds are rectified by abstaining from living meat as defined by the Torah. This in turn inspires gentle and respectful practices, such as those directed towards maintaining the environment.
A functioning judicial system corresponds to malchut, the lowest sefira, which rules in supremacy but is selflessly devoted to public service. This is the responsibility of good government. Our sages state, "War comes to the world through the delay of justice, the perversion of justice, and the teaching of Torah not in accordance with Jewish Law". (Avot 5:8) When both Jews and non-Jews can learn Torah without distortion of its halachic (Jewish legal) meaning, true peace becomes possible. This includes recognition of the principle that Jews can be judged only according to Torah law, no matter where in the world, and that non-Jews in Eretz Yisrael are considered according to the Seven Noahide Laws by the Jews there, with no sovereign jurisdiction of their own.