Why is it that suffusing the vital soul with Ein Sof-light and banishing the impure kelipot from the vital soul produces a parallel effect on the entire world?

For the community of Israel, comprising 600,000 particular souls, is the general source of vitality for the world as a whole, since the world was created for the sake of these souls.

כִּי כְּלָלוּת יִשְׂרָאֵל, שֶׁהֵם שִׁשִּׁים רִבּוֹא נְשָׁמוֹת פְּרָטִיּוֹת, הֵם כְּלָלוּת הַחַיּוּת שֶׁל כְּלָלוּת הָעוֹלָם, כִּי בִּשְׁבִילָם נִבְרָא,

Each specific one of them contains and to each is related the vitality of one-six-hundred-thousandth part of the entire world.

וְכָל פְּרָט מֵהֶם הוּא כּוֹלֵל וְשַׁיָּיךְ לוֹ הַחַיּוּת שֶׁל חֵלֶק אֶחָד מִשִּׁשִּׁים רִבּוֹא מִכְּלָלוּת הָעוֹלָם

This [part of the world] depends on his vital soul for its elevation to G-d through [the vital soul’s] own elevation.

הַתָּלוּי בְּנַפְשׁוֹ הַחִיּוּנִית, לְהַעֲלוֹתוֹ לַה' בַּעֲלִיָּיתָהּ,

This means that one elevates “his” portion of the world by his partaking of this world for the requirements of his body and vital soul in the service of G-d. By using the objects of this world that one’s body and vital soul need for the sake of serving G-d, one elevates his portion of the world.

דְּהַיְינוּ, בְּמַה שֶּׁמִּשְׁתַּמֵּשׁ מֵעוֹלָם הַזֶּה לְצוֹרֶךְ גּוּפוֹ וְנַפְשׁוֹ הַחִיּוּנִית לַעֲבוֹדַת ה',

For example: eating, drinking, and the like, one’s dwelling, and all his utensils.

כְּגוֹן, אֲכִילָה וּשְׁתִיָּה וְדוֹמֵיהֶם, וְדִירָה וְכָל כְּלֵי תַּשְׁמִישָׁיו.

But surely there are more than 600,000 souls; besides, it is quite impossible for one person to use a six-hundred-thousandth of the entire world.

These 600,000 particular souls, however, are “roots”; and, like a root from which grows numerous branches, each root-soul subdivides into 600,000 sparks, each spark being one neshamah.

אֶלָּא שֶׁשִּׁשִּׁים רִבּוֹא נְשָׁמוֹת פְּרָטִיּוֹת אֵלּוּ הֵן שָׁרָשִׁים, וְכָל שֹׁרֶשׁ מִתְחַלֵּק לְשִׁשִּׁים רִבּוֹא נִיצוֹצוֹת, שֶׁכָּל נִיצוֹץ הוּא נְשָׁמָה אַחַת,

Similarly with the nefesh and ruach in each of the four Worlds—Atzilut, Beriah, Yetzirah, and Asiyah. In each of these four Worlds are found all three soul-levels—nefesh, ruach, and neshamah.

וְכֵן בְּנֶפֶשׁ וְרוּחַ, בְּכָל עוֹלָם מֵאַרְבַּע עוֹלָמוֹת אֲצִילוּת־בְּרִיאָה־יְצִירָה־עֲשִׂיָּה.