(6) I the LORD, in My grace, have summoned you, And I have grasped you by the hand. I created you, and appointed you A covenant people, a light of nations—
(א) לברית עם. לקיום כל עם ועם כי בעבורך מתקיים כל העולם וכל ברית הוא ענין קיום וכן תהיה גם כן לאור גוים, כמו שאמר והלכו גוים לאורך, והאור הוא התורה שתצא להם מציון, וישראל יהיו קיום האומות על שני פנים האחד שיהיה שלום בעבורם בכל הגוים כמו שאמר על המשיח ודבר שלום לגוים, ואמר והוכיח לעמים רבים, וכתתו חרבותם לאתים וגו', השנית כי בסבת ישראל יהיו הגוים שומרים שבע מצות וילכו בדרך טובה כמו ויורנו מדרכיו ונלכה באורחותיו וגו':
A Covenant with the Nation: To sustain the existence of all the nations because through you, the world is continuing to exist. The idea of a covenant is a pact that sustains an existence, and so the brit itself will be a light unto the nations like it says: "The nations will go by your light". The light is the Torah that goes out of Zion. Israel will sustain the nations of the world through two ways: One is that there will be peace amongst all the nations because of the Jewish people. Referring to the Messiah, it says "he will speak words of peace to the nations, and he will rebuke many nations, and their swords will be beaten into plowshares." The second reason is that because of the Jewish people, the other nations will keep the seven Noahide laws and they will go in a good path, like it says: And He will teach us His ways and we shall walk in His paths"
Do you want to be a light unto the nations? Turn on the light in your house first.
Michael Broyde, from Tikkun Olam: Social Responsibility in Jewish Thought and Law
Rabbi Schneerson’s view is unique in that he not only assumes that Maimonides is correct in ruling that there is a general obligation to compel gentiles to observe Noachide law, but he also assumes that the obligation to compel observance includes within it the obligation to persuade. Rabbi Schneerson thus extends to the obligation to cover a much greater area than any other rabbinical authority, both in terms of the responsibility to do so and in the means by which to do so.
Excerpts from "Is Social Activism Destroying American Judaism?" by Tzvi Freeman, Chabad.org
Tikkun Olam, then, means getting to the source of the problem and fixing up this concealment. Tikkun Olam is the world discovering itself. Discovering that it is not a junkyard or a no-man’s wasteland. Discovering that its beauty is endless and its wisdom unfathomable, because it is the ultimate expression of the mystery
the divine.
G‑d is not silent because the world does not matter to Him. He is simply making room for us, so that we can have a part in improving His world. That’s why we were placed in this world—to grapple with the apparent absence of G‑d, and to discover Him even in His act of hiding Himself. Once that is accomplished, there can no longer be any evil or suffering—because the root cause will be gone.
As individuals, they simply could not stand idly by (watching people suffer). Because if that’s what comes your way, it’s up to you to do something. After all, wisdom cannot flourish in a world at war with itself, the beauty of life cannot be told when children are starving.
This is what Maimonides is saying when he describes, in the very last Halachah of his Code, the ultimate state of this world, an era when …there will be neither famine or war, envy or competition for good will flow in abundance and all the delights will be freely available as dust. The occupation of the entire world will be solely to know G‑d.
Meaning: What is the point of eliminating famine, war, envy, and competition? So that the entire world can be thoroughly engaged in the true purpose of the human being—to know our Creator.
Yet all this is with a mighty caveat: First, ensure your own house is tidy.
Not just because you can’t help someone else with their oxygen mask until you’ve put on your own. That’s also true. But there’s a much greater reason: If it’s your house, it’s your primary divine assignment in this world. If so, for you, nothing can be more important.
Nothing can be more important for a Jew than building a Jewish home, ensuring the children and grandchildren will be good Jews, reaching out to other Jews, learning and teaching Torah, doing as many mitzvahs as possible. There is no greater contribution to tikkun olam.