פניני הלכה ברכות א:ג
משמעות לשון 'ברכה' – תוספת וריבוי. כמו שנאמר (שמות כג, כה): "ובירך את לחמך", והכוונה יוסיף וירבה את לחמך. וכן נאמר (דברים ז, יג): "וַאֲהֵבְךָ וּבֵרַכְךָ וְהִרְבֶּךָ וּבֵרַךְ פְּרִי בִטְנְךָ וּפְרִי אַדְמָתֶךָ דְּגָנְךָ וְתִירֹשְׁךָ וְיִצְהָרֶךָ שְׁגַר אֲלָפֶיךָ וְעַשְׁתְּרֹת צֹאנֶךָ עַל הָאֲדָמָה אֲשֶׁר נִשְׁבַּע לַאֲבֹתֶיךָ לָתֶת לָךְ", והכוונה שירבה ויוסיף על פרי בטנך ואדמתך. ואם כן מהו שאנו מברכים את ה', הלא הוא שלם ואין סופי, ומה אפשר להוסיף ולהרבות בו? אלא שהכוונה לריבוי גילוי שכינתו בעולם, שעל ידי שאנו נהנים מעולמו ויודעים שהכל ממנו, ואומרים זאת, מתווסף גילוי שכינתו בעולם. ואם כן באמירת הברכה איננו מתפללים עליו כביכול, אלא מציינים עובדה, שבזה שאנו יודעים שהכל בא ממנו, מתרבה גילויו בעולם (נפש החיים שער ב', פרקים ב-ד).
Peninei Halacha, Brachot 1:3
The language of "blessing" refers to "adding on" or "increasing." As it says in Shemot 23:25, "and [God] will bless your bread," and the intent is that God will increase the amount of bread you have. Or as it says in Devarim 7:13, "He will favor you and bless you and multiply you; He will bless the issue of your womb and the produce of your soil, your new grain and wine and oil, the calving of your herd and the lambing of your flock, in the land that He swore to your fathers to assign to you" and the intent is that [God] will increase and add on to the "produce of your womb" and your land. And if this is the case, why is it that we "bless God?" Isn't it the case that God is infinite? How could it be possible to add on to God? Rather, the intent is to increase our awareness of God's presence in the world, for through our making explicit and pronouncing enjoyment of God's world and knowledge that everything comes from God, we add on to our "awareness" of God. This being the case, when we say a blessing we are not "praying" rather we are indicating a fact, and through our emphasizing that everything comes from God, we increase our awareness of God in the world (Nefesh Hachayim, Sha'ar 2, Chapters 2-4)
The doctrine of prayer as a social act is the product of what may be called "the sociological fallacy," according to which the individual has no reality except as a carrier of ideas and attitudes that are derived from group existence. Applied to Jewish faith, it is a total misunderstanding of the nature of Jewish faith to overemphasize the social or communal aspect. It is true that a Jew never worships as an isolated individual but as a part of the people Israel. Yet it is within the heart of every individual that prayer takes place. It is a personal duty, and an intimate act which cannot be delegated to either the cantor or to the whole community. We pray with all of Israel, and everyone of us by himself. Contrary to sociological theories, individual prayer came first, while collective prayer is a late phenomenon which is not even mentioned in the Bible
http://www.rabbinicalassembly.org/sites/default/files/public/resources-ideas/cj/classics/9-7-11-b2school/heschel-1953.pdf
מִי שֶׁבֵּרַךְ אֲבוֹתֵינוּ אַבְרָהָם יִצְחָק וְיַעֲקֹב ואמתינו שרה רבקה רחל ולאה, הוּא יְבָרֵךְ וִירַפֵּא אֶת (פלוני בן פלונית), הַקָּדוֹשׁ בָּרוּךְ הוּא יִמָּלֵּא רַחֲמִים עָלָיו לְהַחֲלִימוֹ וּלְרַפְּאֹתוֹ וּלְהַחֲזִיקוֹ וּלְהַחֲיוֹתוֹ, וְיִשְׁלַח לוֹ מְהֵרָה רְפוּאָה שְׁלֵמָה מִן הַשָּׁמַיִם בְּתוֹךְ שְׁאָר חוֹלֵי יִשְׂרָאֵל, רְפוּאַת הַנֶּפֶשׁ וּרְפוּאַת הַגּוּף, הַשְׁתָּא בַּעֲגָלָא וּבִזְמַן קָרִיב. וְנֹאמַר אָמֵן:
God who blessed our ancestors, Abraham Isaac and Jacob, Sarah, Rebecca Rachel and Leah, may God bless and heal the following:
The Holy Blessed one may have mercy on him, to bring recovery, healing, strength, and vitality, and send to him speedily a full healing, amongst all of the sick people of Israel, a healing of body and a healing of spirit, speedily, in our time, soon. And we say, Amen.