The question of why the world exists at all opens with a foundational rabbinic teaching cited by Tanya, Part I; Likkutei Amarim 36: the Holy One desired an abode in the lower worlds, and therefore the ultimate purpose of all the descending chain of worlds points not upward but downward — to this physical, material world — so that when the sitra achara is subdued and darkness is turned to light, Divine light shall shine precisely here.
Yeshayahu 45:18 anchors this in prophetic speech: God did not create the world as chaos — לֹא־תֹהוּ בְרָאָהּ — but fashioned and established it לָשֶׁבֶת, to be inhabited and settled, a declaration that purposeful, engaged dwelling in physical reality is itself the telos of creation.
Human beings are the vehicle for actualizing this purpose: Netivot Olam, Netiv HaTorah 15 teaches that the human being, called אדם on account of the אדמה from which he comes, is created in potential — like earth sown with seed — and Torah and good deeds are the fruit by which that potential is brought from כֹּחַ into פֹּעַל, from latency into full actualization.
Kiddushin 40b records the definitive ruling of the Sages assembled at Lod: study is greater than action — but only because study leads to action; the entire weight of Torah learning is measured by its capacity to generate deed in the world.
Tanya, Part I; Likkutei Amarim 37 makes explicit that the ultimate fulfillment — the revelation of Ein Sof light in this material world — depends on our actions and service throughout the duration of exile, because through performing a commandment in physical matter that was previously under the dominion of kelipat nogah, a person draws Divine light downward to be clothed in the corporeality of this world.
רמח"ל, מאמר הגאולה develops this further, teaching that the great repair of the Messianic era is above all a repair of the body alongside the soul — and that the glory of holiness is in fact greater in the body than in the soul, since the soul was sent into the world precisely in order to repair the body, which stands on the lowest rung.
Mesillat Yesharim 26 draws a sharp distinction between the person of purity, whose physical acts remain merely necessary, and the person of holiness, for whom even physical deeds become matters of genuine sanctity — as the eating of Temple offerings is itself a positive commandment that effects atonement.
Tomer Devorah 1 frames the entire project in terms of resemblance to the Creator: the essence of the Divine image and likeness is not bodily form but action, and whoever does not resemble his Creator in deeds betrays the form — beautiful form with ugly deeds — so that imitating the thirteen attributes of Divine mercy in actual conduct is the very definition of living in the Divine image.
Orot HaTorah 2:1 adds that every person who studies Torah draws its wisdom from potential into actuality from the side of his own soul, and thereby genuinely enlarges the Torah itself — since the Blessed One desires that Torah be magnified more and more through its connection to each unique individual soul.
Duties of the Heart, Fourth Treatise on Trust 4 insists that trust in Providence is not passivity: even though a person's end is determined by Divine decree, he is obligated to pursue the means of life — food, clothing, shelter — and may not leave this to Heaven, because engagement with the world through natural means is itself the required path.
Pirkei Avot 2:12 gives practical shape to the whole vision: let all your deeds be for the sake of Heaven — וְכָל מַעֲשֶׂיךָ יִהְיוּ לְשֵׁם שָׁמָיִם — so that the turn toward action in the world is not a departure from the sacred but its fullest expression, with Mishnah Berurah 1:1 echoing that man was created precisely for the service of his Creator, citing Yeshayahu 43:7: all who are called by My name, I created for My glory.