The mitzvah of tzitzit is explained as a practical reminder that awakens a person to remember and perform the commandments. The garment's visible sign functions like a servant's identifying seal by keeping the master's commands continually before the servant.
שֹׁרֶשׁ הַמִּצְוָה נִגְלֶה בַּכָּתוּב, שֶׁהוּא לְמַעַן נִזְכֹּר כָּל מִצְוֹת הַשֵּׁם תָּמִיד, וְאֵין דָּבָר בָּעוֹלָם יוֹתֵר טוֹב לְזִכָּרוֹן, כְּמוֹ נוֹשֵׂא חוֹתָם אֲדוֹנָיו קָבוּעַ בִּכְסוּתוֹ אֲשֶׁר יְכַסֶּה בָּהּ תָּמִיד, וְעֵינָיו וְלִבּוֹ עָלָיו כָּל הַיּוֹם, וְזֶהוּ שֶׁנֶּאֱמַר בּוֹ בַּכָּתוּב (במדבר טו לט) וּזְכַרְתֶּם אֶת כָּל מִצְוֹת יְיָ. וְאָמְרוּ זִכְרוֹנָם לִבְרָכָה (תנחומא קורח יב) כִּי מִלַּת צִיצִית תִּרְמֹז לְתַרְיָ"ג מִצְוֹת עִם צֵרוּף שְׁמֹנָה חוּטִין שֶׁבַּצִּיצִית וַחֲמִשָּׁה קְשָׁרִין שֶׁבּוֹ. וְעוֹד אוֹמֵר לִי לִבִּי, שֶׁיֵּשׁ בּוֹ רֶמֶז וְזִכָּרוֹן, שֶׁגּוּפוֹ שֶׁל אָדָם וְנַפְשׁוֹ הַכֹּל לְהַשֵּׁם בָּרוּךְ הוּא, כִּי הַלָּבָן רֶמֶז לַגּוּף שֶׁהוּא מִן הָאָרֶץ שֶׁנִּבְרֵאת מִן הַשֶּׁלֶג שֶׁהוּא לָבָן, כִּדְאַשְׁכְּחַן בְּפִרְקֵי רַבִּי אֱלִיעֶזֶר (פ"ג) הָאָרֶץ מֵהֵיכָן נִבְרֵאת? מִשֶּׁלֶג שֶׁתַּחַת כִּסֵּא הַכָּבוֹד, וְחוּטִין רֶמֶז אֶל הַגּוּף, כְּעִנְיַן אָמְרָם כִּי תְּחִלַּת בְּרִיאַת הַגּוּף הוּא כְּעֵין חוּטִין, וּכְמוֹ שֶׁאָמְרוּ זִכְרוֹנָם לִבְרָכָה פֶּרֶק הַמַּפֶּלֶת (נדה כה, ב) אָמַר רַב עַמְרָם תָּנָא שְׁנֵי יַרְכוֹתָיו כִּשְׁנֵי חוּטִין שֶׁל זְהוֹרִית, שְׁנֵי זְרוֹעוֹתָיו כִּשְׁנֵי חוּטִין שֶׁל זְהוֹרִית, וְהַתְּכֵלֶת אֲשֶׁר עֵינוֹ כְּעֵין הָרָקִיעַ יִרְמֹז לַנֶּפֶשׁ שֶׁהִיא מִן הָעֶלְיוֹנִים, וְלָזֶה רָמְזוּ בְּאָמְרָם (מנחות מז ב) מָה נִשְׁתַּנָּה תְּכֵלֶת מִכָּל מִינֵי צִבְעוֹנִין? מִפְּנֵי שֶׁהַתְּכֵלֶת דּוֹמָה לַיָּם, וְהַיָּם דּוֹמֶה לָרָקִיעַ, וְהָרָקִיעַ דּוֹמֶה לְכִסֵּא הַכָּבוֹד, שֶׁנֶּאֱמַר (שמות כד י) וַיִּרְאוּ אֵת אֱלֹהֵי יִשְׂרָאֵל וְגוֹ' וְאוֹמֵר (יחזקאל א כו) כְּמַרְאֵה אֶבֶן סַפִּיר דְּמוּת כִּסֵּא. וְתַחַת כִּסֵּא הַכָּבוֹד מָקוֹם שֶׁנַּפְשׁוֹת הַצַּדִּיקִים גְּנוּזוֹת שָׁם, וּמִפְּנֵי כֵן אָמְרוּ (מנחות לט א) שֶׁכּוֹרְכִין חוּט הַתְּכֵלֶת עַל הַלָּבָן, שֶׁהַנֶּפֶשׁ הִיא הָעֶלְיוֹנָה וְהַגּוּף תַּחְתּוֹן. וְאָמְרוּ שֶׁעוֹשִׂין מִמֶּנּוּ שֶׁבַע כְּרִיכוֹת אוֹ שְׁלֹשׁ עֶשְׂרֵה לִרְמֹז הָרְקִיעִים וְהָאֲוִירִים שֶׁבֵּינֵיהֶם, וּכְמוֹ שֶׁאָמְרוּ (שם) תַּנָּא הַפּוֹחֵת לֹא יִפְחֹת מִשֶּׁבַע, כְּנֶגֶד שִׁבְעָה רְקִיעִים, וְלֹא יוֹסִף עַל שְׁלֹשׁ עֶשְׂרֵה כְּנֶגֶד שִׁבְעָה רְקִיעִים וְשִׁשָּׁה אֲוִירִים שֶׁבֵּינֵיהֶם.
The root of the commandment is revealed in the verse: It is in order that we always remember all of the commandments of God. And there is no better reminder in the world than carrying the seal of the Master on the clothes that one wears at all times, as a person is [always attentive] to his clothes. And this is what is stated in the verse (Numbers 15:39), “and you will recall all the commandments of the Lord.” And they, may their memory be blessed, said (Midrash Tanchuma, Korach 12) that the word “tsitsit” alludes to the six hundred and thirteen commandments (in the numerical equivalent of the letters) when combined with the eight strings of the fringes and their five knots. And my heart also tells me that there is a reminder and allusion here that the soul and body of man all belong to God, blessed be He. As the white portion corresponds to the body which is from the land, which was made from the snow, which is white, as we find in Pirkei D'Rabbi Eliezer 3, “From where is the land from? From the snow that is under the Holy Throne.” And the threads [also] allude to the body, as the matter that they said, that the initial formation of a body is like threads. [It is] as they, may their memory be blessed, said (Niddah 25b), “Rabbi Amram said, ‘The two thighs are like two strands of crimson, the two forearms are like two strands of crimson.’” The blue (tekhelet), the appearance of which is like the appearance of the sky, hints to the soul which is from the upper beings. And they hinted to this in their saying (Menachot 47b), “What [makes] tekhelet different than all other colors? Because tekhelet is like the sea, and the sea is like the sky, and the sky is like the Throne of Glory, as it is stated (Exodus 24:10), ‘And they saw the God of Israel, etc.’ and it states (Ezekiel 1:26), ‘The Throne appeared as sapphire stone’” — and the souls of the righteous are stored underneath the Throne. And because of this, they said (Menachot 39a) that we wrap the string of tekhelet around the white, as the soul is above and the body below. They said that we make seven or thirteen windings [around the white strings] to allude to the heavens and the divisions between them. And it is as they said (Menachot 39a), “It is taught, ‘One who wishes to do fewer should not do fewer than seven, nor should he add more than thirteen, corresponding to the seven heavens and the six air-spaces between them.’”