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What is Bracha? (Hint: "Blessing" is Not The Answer)
What is bracha? Yes, we translate it as "blessing," but what does that mean?
Every day, we bless God, say He is blessed, and ask Him for blessing. If we don't really know what we're saying, then we're missing out on something pretty big.
תַּנְיָא, אָמַר רַבִּי יִשְׁמָעֵאל בֶּן אֱלִישָׁע: פַּעַם אַחַת, נִכְנַסְתִּי לְהַקְטִיר קְטוֹרֶת לִפְנַי וְלִפְנִים, וְרָאִיתִי אַכְתְּרִיאֵל יָהּ ה׳ צְבָאוֹת, שֶׁהוּא יוֹשֵׁב עַל כִּסֵּא רָם וְנִשָּׂא, וְאָמַר לִי: ״יִשְׁמָעֵאל בְּנִי, בָּרְכֵנִי!״ אָמַרְתִּי לוֹ: ״יְהִי רָצוֹן מִלְּפָנֶיךָ, שֶׁיִּכְבְּשׁוּ רַחֲמֶיךָ אֶת כַּעַסְךָ, וְיִגּוֹלּוּ רַחֲמֶיךָ עַל מִדּוֹתֶיךָ, וְתִתְנַהֵג עִם בָּנֶיךָ בְּמִדַּת הָרַחֲמִים, וְתִכָּנֵס לָהֶם לִפְנִים מִשּׁוּרַת הַדִּין״. וְנִעְנַע לִי בְּרֹאשׁוֹ. וְקָמַשְׁמַע לַן, שֶׁלֹּא תְּהֵא בִּרְכַּת הֶדְיוֹט קַלָּה בְּעֵינֶיךָ.
Similarly, it was taught in a baraita that Rabbi Yishmael ben Elisha, the High Priest, said: Once, on Yom Kippur, I entered the innermost sanctum, the Holy of Holies, to offer incense, and in a vision I saw Akatriel Ya, the Lord of Hosts, one of the names of God expressing His ultimate authority, seated upon a high and exalted throne (see Isaiah 6).
And He said to me: Yishmael, My son, bless Me.
I said to Him the prayer that God prays: “May it be Your will that Your mercy overcome Your anger,
and may Your mercy prevail over Your other attributes,
and may You act toward Your children with the attribute of mercy,
and may You enter before them beyond the letter of the law.”
The Holy One, Blessed be He, nodded His head and accepted the blessing. This event teaches us that you should not take the blessing of an ordinary person lightly. If God asked for and accepted a man’s blessing, all the more so that a man must value the blessing of another man.
Here, our question is born. What on earth does it mean that Rabbi Yishmael ben Elisha not only blessed God, but God asked him to do so?! Well ... don't we bless God every single day, countless times a day, for all sorts of different things?
Rav Chaim of Volozhin will kick us off in his Nefesh HaChayim.

(ב) אבל האמת כי ברוך פירושו לשון תוספת וריבוי וכענין קח נא את ברכתי גו'. וברך את לחמך. וברך פרי בטנך וגו'. והרבה כיוצא במקרא. שא''א לפרשם לשון תהלה ושבח אלא לשון תוספת ורבוי.

(2) However, the truth is that ba-rookh, its meaning is an expression of increase and expansion, and consonant with the context of (Berakhot 7a) “accept, please, my b’rakha…” (B’reishit 33:11), and “and He will bless your food” (Shemot 23:25), and “and He will bless the fruit of your womb…” (D’varim 7:13), and many others similar to these in the text, so that it’s impossible to translate them as expressions of attributing glory and giving praise; rather [it’s] an expression of increase and expansion.

Nefesh HaChayim is telling us that "blessing" refers to an increase or expansion of something. Does that mean we're "increasing" or "expanding" God when we bless Him?

(ה) אמנם ענין הברכה לו ית''ש. אין הכוונה לעצמות אדון יחיד ב''ה כביכול. חלילה וחלילה. כי הוא מרומם מעל כל ברכה. אבל הענין כמ''ש בזו' דקב''ה סתים וגליא. כי עצמות א''ס ב''ה סתים מכל סתימין ואין לכנותו ח''ו בשום שם כלל אפילו בשם הוי''ה ב''ה ואפי' בקוצו של יו''ד דבי'.

(5) However the context of blessing Him (blessed be His name), the intention is not [aimed] towards the Essence (so to speak) of the One Master (blessed is He), (never! never!), for He is far, far above any blessing. Rather the context is as is stated in the Zohar (Ehmore 98, and in other places), that the Holy One (blessed be He) is [both] revealed and hidden. For the Essence of the Ein Sofe (blessed is He) is the most hidden of the hiddens, and can’t be assigned any name at all, not even the name YHV”H (blessed is He), nor even to the top thorn of its letter Yud.

(ו) (ואף גם מה שבז''הק מכנהו ית' בשם אין סוף איננו כנוי עליו ית''ש אלא הכוונה על השגתנו אותו מצד כחות הנשפעים מאתו בהתחברותו ברצונו להעולמות. ולזאת כנוהו א''ס ולא אין ראשית. כי באמת מצד עצמותו ית''ש אין לו לא סוף ולא ראשית. רק מצד השגתינו כחותיו ית'. הלא כל השגתינו הוא רק ראשית. אבל אין סוף להגיע בהשגה להשיג את כחותיו ית' הנשפעים.)

(6) And though the Zohar refers to Him (blessed be He) with the name Ein Sofe, it’s not a descriptive name for Him (blessed be His name). Rather the intention is relative to how we perceive Him, from the perspective of the forces that are affected by Him via his purposeful relationship with the worlds. And for this reason He is referred to as “Without End” and not “Without Beginning”, for in truth from the perspective of His Essence (blessed be His name) He has no end and no beginning; [it’s] only from our perspective of His powers (blessed be He). It’s that all of our understanding is just a beginning, but there’s no final destination at which we can arrive with an understanding of His powers (blessed be His name) that influence [the world].

Ah, we are not doing anything to God Himself, rather we are changing our experience and awareness of God. We will look further, but here is a helpful analogy:
Imagine you are sitting in a room with boarded-up windows during the day, completely enveloped in darkness. As you uncover more windows, the room will become increasingly brighter. Are you changing the sun? No! You're changing your experience of the sun and its light.

(ב) א כִּי הַשֵּׁם יִתְבָּרַךְ מֵחֲמַת רַחֲמָנוּתוֹ בָּרָא אֶת הָעוֹלָם, כִּי רָצָה לְגַלּוֹת רַחֲמָנוּתוֹ, וְאִם לֹא הָיָה בְּרִיאַת הָעוֹלָם עַל מִי הָיָה מַרְאֶה רַחֲמָנוּתוֹ. וְעַל כֵּן בָּרָא אֶת כָּל הַבְּרִיאָה מִתְּחִלַּת הָאֲצִילוּת, עַד סוֹף נְקֻדַּת הַמֶּרְכָּז שֶׁל עוֹלָם הַגַּשְׁמִי, כְּדֵי לְהַרְאוֹת רַחֲמָנוּתוֹ.

(ג) וְכַאֲשֶׁר רָצָה הַשֵּׁם יִתְבָּרַךְ לִבְרֹא אֶת הָעוֹלָם, לֹא הָיָה מָקוֹם לְבָרְאוֹ, מֵחֲמַת שֶׁהָיָה הַכֹּל אֵין סוֹף, עַל־כֵּן צִמְצֵם אֶת הָאוֹר לִצְדָדִין, וְעַל יְדֵי הַצִּמְצוּם הַזֶּה נַעֲשָׂה חָלָל הַפָּנוּי, וּבְתוֹךְ הֶחָלָל הַפָּנוּי הַזֶּה, נִתְהַוּוּ כָּל הַיָּמִים וְהַמִּדּוֹת, שֶׁהֵם בְּרִיאַת הָעוֹלָם (כמ"ש בעץ חיים בתחילתוֹ).

(ה) כִּי הֶחָלָל הַפָּנוּי הוּא עַל־יְדֵי הַצִּמְצוּם, שֶׁכִּבְיָכוֹל צִמְצֵם אֱלֹקוּתוֹ מִשָּׁם, וְאֵין שָׁם אֱלֹקוּת כִּבְיָכוֹל, כִּי אִם לֹא כֵן אֵינוֹ פָּנוּי, וְהַכֹּל אֵין סוֹף, וְאֵין מָקוֹם לִבְרִיאַת הָעוֹלָם כְּלָל. אֲבָל בֶּאֱמֶת לַאֲמִתּוֹ, בְּוַדַּאי אַף־עַל־פִּי־כֵן יֵשׁ שָׁם גַּם כֵּן אֱלֹקוּת, כִּי בְּוַדַּאי אֵין שׁוּם דָּבָר בִּלְעֲדֵי חִיּוּתוֹ, וְעַל־כֵּן אִי אֶפְשָׁר לְהַשִּׂיג כְּלָל בְּחִינַת חָלָל הַפָּנוּי עַד לֶעָתִיד לָבוֹא:

(2) God created the world as a consequence of His compassion. For He wanted to reveal His compassion, and if Creation had not taken place, to whom would He have shown His compassion? He therefore created the entire creation, from the inception of Atzilut all the way down to the center point of the corporeal world, in order to display His compassion.

(3) Yet when God wanted to create the world, there was no place in which to create it, since there was nothing but Ein Sof (the Infinite One). He therefore contracted the Light to the sides, and through this contraction the Vacated Space was made. Then, within this Vacated Space, all time and space came into existence—this being the creation of the world {as explained at the beginning of Etz Chaim} .

(5) The Vacated Space is the result of the contraction; that [God], so to speak, withdrew His Godliness from that place. Thus there is, so to speak, no Godliness there. Were it not so, it would not be vacated. There would then be nothing but Ein Sof, with no place whatsoever for the world’s creation. However the actual truth is that, even so, there is surely Godliness there as well. For there is surely nothing without His life-force. This is why it is not at all possible to comprehend the concept of the Vacated Space until the Future.

This short passage is definitely a simplified form of a very rich, complex, and important idea in Kabbalah, but the main takeaway is this: God is found in every single thing in the world. He wants us to reveal Him there.

(א) החכם השלם, שאלת: מהו ענין הברכות? שהברכה תוספת טובה, ומה יוסיף עבד לאדוניו? באמת לשון ברכה תוספת וריבוי הוא, והוא מלשון ברכות המים.

(1) To the wise, complete person: You asked, "What are blessings? The term 'berachah[blessing]' ‎refers to increased good, but what can a servant add to his Master?" In truth, the word "berachah" ‎is an expression of increase and multiplication, like the expression, "springs [bereichot] of water".

Putting this all together, we see that when we "bless God," we are increasing our awareness of Him in the world. When we perceive more of God, we are then able to receive His overflow of goodness like collecting water from a spring, a brecha in Hebrew.

Of course, there are certain applications of this that can be further fleshed out, but it seems best not to exhaust the length of this sheet. The way for one to apply this concept in other areas of how "blessing" is used should be relatively easy, with God's help.