Shame and Humiliation According to Various Jewish Sources

מתני׳ החובל בחבירו חייב עליו משום חמשה דברים בנזק בצער בריפוי בשבת ובושת:

MISHNA: One who injures another is liable to pay compensation for that injury due to five types of indemnity: He must pay for damage, for pain, for medical costs, for loss of livelihood, and for humiliation.
וַיֹּ֨אמֶר מֹשֶׁ֣ה אֶל־הָעָם֮ אַל־תִּירָאוּ֒ כִּ֗י לְבַֽעֲבוּר֙ נַסּ֣וֹת אֶתְכֶ֔ם בָּ֖א הָאֱלֹהִ֑ים וּבַעֲב֗וּר תִּהְיֶ֧ה יִרְאָת֛וֹ עַל־פְּנֵיכֶ֖ם לְבִלְתִּ֥י תֶחֱטָֽאוּ׃
Moses answered the people, “Be not afraid; for God has come only in order to test you, and in order that the fear of Him may be ever with you, so that you do not go astray.”
תַּנְיָא בַּעֲבוּר תִּהְיֶה יִרְאָתוֹ עַל פְּנֵיכֶם זוֹ בּוּשָׁה לְבִלְתִּי תֶחֱטָאוּ מְלַמֵּד שֶׁהַבּוּשָׁה מְבִיאָה לִידֵי יִרְאַת חֵטְא מִיכָּן אָמְרוּ סִימָן יָפֶה בְּאָדָם שֶׁהוּא בַּיְישָׁן אֲחֵרִים אוֹמְרִים כׇּל אָדָם הַמִּתְבַּיֵּישׁ לֹא בִּמְהֵרָה הוּא חוֹטֵא וּמִי שֶׁאֵין לוֹ בּוֹשֶׁת פָּנִים בְּיָדוּעַ שֶׁלֹּא עָמְדוּ אֲבוֹתָיו עַל הַר סִינַי
§ It is taught in a baraita: “That His fear may be upon your faces” (Exodus 20:17); this is referring to shame, as shame causes one to blush. “That you not sin” (Exodus 20:17) teaches that shame leads to fear of sin. From here the Sages said: It is a good sign in a person that he is one who experiences shame. Others say: Any person who experiences shame will not quickly sin, and conversely, one who does not have the capacity to be shamefaced, it is known that his forefathers did not stand at Mount Sinai.
אמר שלשה סימנים יש באומה זו הרחמנים והביישנין וגומלי חסדים רחמנים דכתיב (דברים יג, יח) ונתן לך רחמים ורחמך והרבך ביישנין דכתיב (שמות כ, כ) בעבור תהיה יראתו על פניכם גומלי חסדים דכתיב (בראשית יח, יט) למען אשר יצוה את בניו ואת ביתו וגו' כל שיש בו שלשה סימנים הללו ראוי להדבק באומה זו
David said: There are three distinguishing marks of this nation, the Jewish people. They are merciful, they are shamefaced, and they perform acts of kindness.
They are merciful, as it is written: “And He will give you mercy, and have mercy upon you and multiply you” (Deuteronomy 13:18); not only will God have mercy upon you, but He will bestow the attribute of mercy upon you.
They are shamefaced, as it is written: “And that His fear shall be upon your faces” (Exodus 20:17), and the fear that is on one’s face is his shame.
They perform acts of kindness, as it is written: “For I have known him, to the end that he may command his children and his household after him, that they may keep the way of the Lord, to practice righteousness and justice” (Genesis 18:19), i.e., to perform acts of kindness.
Whoever has these three distinguishing marks is fit to cleave to this nation. Those who lack these qualities, however, are unfit to be part of the Jewish people. When David saw the cruelty of the Gibeonites, he decreed that they may never enter into the congregation of Israel.

ואח״‎כ חשוב במדת הבושת אשר יחד בה האדם מה גדלה מעלתה ורבה תועלתה ותקנתה ולולא היא לא היו מאכסנים אכסנאי ולא מקיימים דבר ולא ממלאים משאל ולא גומלים חסד ומתרחקים מן הרע בשום דבר עד כי דברים רבים מדברי התורה עושים בעבור הבושת כי רוב מבני אדם לא היו מכבדים את אבותם לולא הבושת כ״‎ש זולתם ולא היו משיבין אבדה ולא נמנעין מעבירה כי כל אשר יעשה מכל אלה הדברים המגונים שזכרנו אינו עושה אותם אלא לאחר שיפשוט כסות הבושת מעליו כמ״‎ש הכתוב (ירמיה ו) גם בוש לא יבושו גם הכלים לא ידעו ואומר (צפניה ג׳:ה׳) ולא יודע עול בשת.

Bachya ibn Pekuda (Written in 1040 CE in present-day Spain)

Afterwards, reflect on the feeling of shame with which man alone has been endowed. How high is its value! How numerous are its uses and advantages. Were it not for this feeling, men would not show hospitality to strangers. They would not keep their promises, grant favors, show kindness, nor abstain from evil in any way. Many precepts of the Torah are fulfilled only out of shame. A large number of people would not honor their parent if it were not for shame, and certainly would fail to show courtesy to others. They would not restore a lost article to its owner, nor refrain from any transgression. For whoever commits any of the disgraceful acts which we have mentioned, does so only when he has cast off the garment of shame. As Scripture said: "Yea they are not at all ashamed, neither know they how to blush" (Yirmiyahu 6:15), and "The sinner knows no shame" (Tzefania 3:5).

לֹ֧א לְמַעַנְכֶ֣ם אֲנִֽי־עֹשֶׂ֗ה נְאֻם֙ אדני יהוה יִוָּדַ֖ע לָכֶ֑ם בּ֧וֹשׁוּ וְהִכָּלְמ֛וּ מִדַּרְכֵיכֶ֖ם בֵּ֥ית יִשְׂרָאֵֽל׃ (ס)
Not for your sake will I act—declares the Lord GOD—take good note! Be ashamed and humiliated because of your ways, O House of Israel!

Rabbi Abraham Joshua Heschel, "Yom Kippur"

We are all failures. At least one day a year we should recognize it. I have failed so often; I am sure those present here have also failed. We have much to be contrite about; we have missed opportunities. The sense of inadequacy ought to be at the very center of the day. [...]

I would strongly advise you to stress and develop this aspect, along with the aspect of contrition. To put contrition another way, develop a sense of embarrassment. The root of any religious faith is a sense of embarrassment, of inadequacy. I would cultivate a sense of embarrassment. It would be a great calamity for humanity if the sense of embarrassment disappeared, if everybody was an all-rightnik, with an answer to every problem. We have no answer to ultimate problems. We really don’t know. In this not knowing, in this sense of embarrassment, lies the key to opening the wells of creativity. Those who have no embarrassment remain sterile. We must develop this contrition or sense of embarrassment.