What is in essence the core, true and purposeful meaning is according to the Tzaddikim and True Sages who have received the tradition back to Moshe Rabbeinu. Now Hevel (breath, vapor, vanity etc.) is a deep matter, being that Breath is the Neshama (breathing, living, etc.) so there are many, many aspects related. For example, here is one. Bringing it to the practical level, when a person makes a sigh for holy aspirations and good things, he draws Life and Goodness toward that thing etc.
https://www.sefaria.org/Likutei_Moharan.109.1.1?lang=bi&with=all&lang2=en
יֵשׁ הֶבֶל אֲשֶׁר נַעֲשָׂה עַל הָאָרֶץ, אֲשֶׁר יֵשׁ צַדִּיקִים שֶׁמַּגִּיעַ אֲלֵיהֶם כְּמַעֲשֵׂה וְכוּ' (קהלת ח׳:י״ד): “Yesh Hevel (There is a vanity) done upon the earth: there are tzaddikim to whom it happens according to the deeds of the wicked, and there are wicked men to whom it happens according to the deeds of the tzaddikim.” (Ecclesiastes 8:14) [See also the essential question of Moshe to H"Y, "Show me Your way" - Why do the righteous suffer yet the wicked prosper?? - Berakhot 7a on Ex. 33:13 https://www.sefaria.org/Berakhot.7a.25?ven=William_Davidson_Edition_-_English&lang=bi]
פֵּרוּשׁ: הֶבֶל, הַיְנוּ הֶבֶל פֶּה הַיּוֹצֵא מֵהַגָּרוֹן, מִגְּנוּחֵי דְּקָגָנַח, כָּל אֶחָד לְפִי עֶרְכּוֹ, צַדִּיקִים יֵלְכוּ וּפוֹשְׁעִים יִכָּשְׁלוּ. The explanation is as follows: Hevel is the hevel -breath of the mouth that comes from the throat, from the sighs that one sighs; each person commensurate with his level, [as in,] “tzaddikim will go,” and “sinners will stumble” (Hoshea 14:10).
יֵשׁ רָשָׁע כָּל יָמָיו, וּמִתְאַנֵּחַ וְנָהּ עַל הֶעָבָר; וְיֵשׁ, חַס וְשָׁלוֹם, צַדִּיק מֵעִקָּרוֹ, וְתוֹהֵא עַל הָרִאשׁוֹנוֹת, וְנָהּ וּמִתְאַנֵּחַ גַּם כֵּן. There is one who was wicked all his days, but sighs and groans over the past. And there is, God forbid, one who was originally righteous, but regrets the former [deeds] and also groans and sighs.
וְהִנֵּה יֵשׁ שְׁנֵי חֲבָלִים: חֶבֶל דִּקְדֻשָּׁה, וּכְנֶגְדּוֹ – דְּטֻמְאָה. וְהַבְּחִירָה חָפְשִׁית, מִי שֶׁמְּקַדֵּשׁ עַצְמוֹ מְקַשֵּׁר עַצְמוֹ בְּחֶבֶל דִּקְדֻשָּׁה, וּלְהֵפֶךְ, חַס וְשָׁלוֹם, מִי שֶׁמְּטַמֵּא עַצְמוֹ מְקַשֵּׁר עַצְמוֹ בְּחֶבֶל דְּטֻמְאָה. Now behold, there are two ropes: the rope of holiness, and counter to it, of impurity. Yet the choice is free. A person who sanctifies himself, binds himself with the rope of holiness. Conversely, God forbid, a person who defiles himself, binds himself with the rope of impurity.
וְהִנֵּה, הַנֹּהַּ וְהָאֲנָחָה הוּא בְּחִינַת מִיתָה בְּגוּף וָנֶפֶשׁ. בְּגוּף – כְּמוֹ שֶׁאָמְרוּ רַבּוֹתֵינוּ זִכְרוֹנָם לִבְרָכָה (ברכות נח:): אֲנָחָה שׁוֹבֶרֶת גּוּפוֹ שֶׁל אָדָם. וּבְנֶפֶשׁ גַּם־כֵּן – כִּי יָדוּעַ מַה שֶּׁכָּתוּב (תהילים ק״ד:כ״ט): תּוֹסֵף רוּחָם יִגְוָעוּן; כִּי קֹדֶם הַמִּיתָה נִתּוֹסֵף רוּחָם, וַאֲזַי יִגְוָעוּן. And behold, groaning and sighing are an aspect of death in body and soul. In body, as our Sages teach: Sighing breaks a man’s body (Berakhot 58b). And also in soul, for known is that which is written (Psalms 104:29), “When You increase their ruach -breath, they perish.” This is because prior to death, “their ruach -breath” increases and then “they perish.”
כְּמוֹ כֵן הַנֹּהַּ וְהָאֲנָחָה, אִם תְּדַקְדֵּק וּתְעַיֵּן בָּהּ, אֵיךְ הִיא נִמְשֶׁכֶת אֶל הַגָּרוֹן, הִיא בִּבְחִינַת תּוֹסֵף רוּחָם, כִּי לְפִי שָׁעָה קַלָּה נִתּוֹסֵף רוּחוֹ, וְכִמְעַט רֶגַע תִּגְוַע וְתֵאָסֵף. The same applies to groaning and sighing. If you investigate and observe how it is drawn to the throat, [you will see that] it is an aspect of “toSeiPh (You increase) their ruach -breath.” For a short while his ruach -breath increases, and but a minute later he [might] perish and be tei’aSeiPh (gathered up).
וְהִנֵּה מִי שֶׁמִּתְאַנֵּחַ וְנָהּ עַל עֲבֵרוֹת שֶׁבְּיָדוֹ, וְרוֹצֶה לָשׁוּב בִּתְשׁוּבָה. אֲזַי בַּאֲנָחָה זוֹ הוּא נִגְוָע וְנֶאֱסָף מִן הָרָע שֶׁהָיָה בְּיָדוֹ, בִּבְחִינַת: תּוֹסֶף רוּחָם יִגְוָעוּן, וְנִדְבָּק אֶל הַקְּדֻשָּׁה. Therefore, when one groans and sighs over the sins he has committed, and wants to return in repentance, then with this sigh he perishes and is gathered up from the evil that was in his hands, as in, “When You increase their ruach -breath, they perish.” And he becomes attached to holiness.
וְכֵן לְהֵפֶךְ, חַס וְשָׁלוֹם, מִי שֶׁנָּהּ וּמִתְאַנֵּחַ עַל הַטּוֹב שֶׁבְּיָדוֹ, וְרוֹצֶה לְדַבֵּק עַצְמוֹ בְּטֻמְאָה, אֲזַי נִגְוָע וְנֶאֱסָף רוּחוֹ דִּקְדֻשָּׁה, וְנִדְבָּק אֶל הַטֻּמְאָה. The reverse is also true, God forbid. When one groans and sighs over the good which he has performed, and wants to attach himself to impurity, then his holy ruach -breath perishes and is gathered up. And he becomes attached to impurity.
וְזֶהוּ: יֵשׁ הֶבֶל – הַיְנוּ הַהֶבֶל פֶּה מֵהַנֹּהַּ וְהָאֲנָחָה שֶׁהוּא נָהּ וּמִתְאַנֵּחַ. This is the meaning of [the opening verse]: There is hevel—That is, the hevel -breath of the mouth from the groan and the sigh which he groans and sighs.
יֵשׁ צַדִּיקִים – שֶׁתּוֹהִין עַל הָרִאשׁוֹנוֹת, וְיוֹצֵא הֶבֶל מִפִּיהֶם מֵהָאֲנָחָה, there are tzaddikim—They regret the former [deeds], and hevel -breath emerges from their mouths from the sighing.
וּמַגִּיעַ אֲלֵיהֶם כְּמַעֲשֵׂה הָרְשָׁעִים – כִּי נִדְבָּקִין אֶל הַסִּטְרָא אָחֳרָא וְהַטֻּמְאָה. to whom it happens according to the deeds of the wicked—This is because they become attached to the Other Side and the impure.
וְיֵשׁ רְשָׁעִים – שֶׁנּוֹהִים וּמְאַנְּחִים, וּמֵהַהֶבֶל שֶׁיּוֹצֵא מִפִּיהֶם and there are wicked men—They groan and sigh, and from the hevel -breath that emerges from their mouth:
מַגִּיעַ אֲלֵיהֶם כְּמַעֲשֵׂה הַצַּדִּיקִים – כִּי נִפְסָקִין מֵהַטֻּמְאָה, וְנִדְבָּקִין אֶל הַקְּדֻשָּׁה. to whom it happens according to the deeds of the tzaddikim—This is because they separate from the impure and become attached to holiness.
וְהַכְּלָל – כִּי אֶת זֶה לְעֻמַּת זֶה, וְצָרִיךְ לִהְיוֹת לוֹ חִיּוּת מֵחֶבֶל מֵאֶחָד שֶׁבִּשְׁנֵיהֶם, וְתֵכֶף שֶׁהוּא נִפְסָק מֵחֶבֶל זֶה, הוּא נִדְבָּק בַּחֶבֶל שֶׁכְּנֶגְדּוֹ. The general principle is this: “[God made] one to contrast the other” (Ecclesiastes 7:14), and a person must get vitality from one or the other of the two ropes. And, no sooner is he separated from one rope, than he becomes attached to the rope which contrasts it.
עַל כֵּן טוֹב לְהַרְגִּיל אֶת עַצְמוֹ לְהִתְאַנֵּחַ עַל מַעֲשָׂיו שֶׁאֵינָם טוֹבִים, וְלִכְסֹף וּלְהִשְׁתּוֹקֵק בְּתֹקֶף אַנְחָתוֹ לָשׁוּב לְהַשֵּׁם יִתְבָּרַךְ, כִּי עַל־יְדֵי אֲנָחָה זֹאת, נִפְסָק מֵחֶבֶל דְּטֻמְאָה, וְנִתְקַשֵּׁר בְּחֶבֶל דִּקְדֻשָּׁה כַּנַּ"ל: It is therefore good to become accustomed to sigh over one’s bad deeds, and to yearn and long, in the midst of one’s sighing, to return to God. For through this sighing, one separates from the rope of impurity and becomes attached to the rope of holiness, as mentioned above.
עוֹד מָצָאתִי מִכְּתַב יַד הַחֲבֵרִים מֵעִנְיַן זֶה, וּמְבֹאָר שָׁם בְּבֵאוּר יוֹתֵר מִגֹּדֶל מַעֲלַת יִקְרַת הָאֲנָחָה דִּקְדֻשָּׁה. כִּי מְבֹאָר שָׁם, שֶׁהָאֲנָחָה שֶׁמְּאַנֵּחַ הָאָדָם עַל עֲווֹנוֹתָיו אוֹ עַל מִעוּט הַשָּׂגָתוֹ, הוּא יוֹתֵר טוֹב מִכַּמָּה סִגּוּפִים וְתַעֲנִיּוֹת. כִּי בְּתַעֲנִית אֵינוֹ מְשַׁבֵּר רַק הַגּוּף לְבַד, אֲבָל בַּאֲנָחָה מְשַׁבֵּר כָּל הַגּוּף, וְגַם מַחֲלִיף אֶת הַנֶּפֶשׁ וְהַחִיּוּת שֶׁלּוֹ מֵרַע לְטוֹב. In addition, I found a manuscript from [Rebbe Nachman’s] students on this topic, in which the tremendous value of the sigh of holiness is explained in greater detail. It is explained there that the sigh which a person sighs over his sins or over his lack of spiritual perception, is more beneficial than many acts of mortification and fasts. This is because a fast breaks only the body, but with a sigh one breaks the whole body and also transforms his soul and life-force from evil to good.
כִּי הַהֶבֶל שֶׁל הָאָדָם, הוּא חֶבֶל הַמְקַשֵּׁר הַנְּשָׁמָה לִמְקוֹם שָׁרְשָׁהּ, לְטוֹב אוֹ לְהֵפֶךְ, חַס וְשָׁלוֹם. וּכְשֶׁמִּתְאַנֵּחַ הוּא בִּבְחִינַת: תּוֹסֵף רוּחָם יִגְוָעוּן, וַאֲזַי נִפְסָק מֵהַחֶבֶל שֶׁהָיָה מְקֻשָּׁר מִתְּחִלָּה וְנִתְקַשֵּׁר לְחֶבֶל אַחֵר כְּפִי הָאֲנָחָה וְכוּ', וְכַנַּ"ל: For a person’s hevel -breath is a chevel (rope) that binds the upper soul to the place of its root—to good, or God forbid, the opposite. And when he sighs, he is in the aspect of “When You increase their ruach -breath, they perish.” At that point, he separates from the rope to which he was originally bound and becomes bound to another rope, commensurate with the sigh [etc. as mentioned. End of Torah 109.]