Satan/Samael (the Angel of Death) has no power on Yom Kippur
אֲמַר לֵיהּ: שָׂטָן בְּיוֹמָא דְכִיפּוּרֵי — לֵית לֵיהּ רְשׁוּתָא לְאַסְטוֹנֵי. מִמַּאי? אָמַר רָמֵי בַּר חָמָא: ״הַשָּׂטָן״ בְּגִמַטְרִיָּא תְּלָת מְאָה וְשִׁיתִּין וְאַרְבְּעָה הָוֵי. תְּלָת מְאָה וְשִׁיתִּין וְאַרְבְּעָה יוֹמֵי — אִית לֵיהּ רְשׁוּתָא לְאַסְטוֹנֵי. בְּיוֹמָא דְכִיפּוּרֵי — לֵית לֵיהּ רְשׁוּתָא לְאַסְטוֹנֵי.
Elijah said to him: Satan, on Yom Kippur, has no license to prosecute. From where is that idea derived? Rami bar Ḥama said: The numerological value of the letters that constitute the word HaSatan is three hundred and sixty four: Heh has a value of five, sin has a value of three hundred, tet has a value of nine, and nun has a value of fifty. Three hundred and sixty-four days of the solar year, which is three hundred and sixty-five days long, Satan has license to prosecute. On the remaining day, Yom Kippur, he has no license to prosecute. Since that day is exalted above all others, there is no room for the accusations of Satan.
This is an example of gematria: Jewish numerology. Each Hebrew letter has a corresponding numerical value and Kabbalists read into those values as mystical insight, comparing them to common numbers found in our world or other Hebrew words with the same value.
In other belief, since Yom Kippur was such a momentous day for the soul, it attracted all sorts of evil spirits looking to cause destruction, from which we have this tradition:
"The blowing of the shofar at the conclusion of the day drives off evil spirits and confuses and confounds the devil."
Jewish Magic and Supersititon, Joshua Trachetenberg
In one Midrash, the scapegoat ritual is actually a bribe to appease Samael/Satan who comes every Yom Kippur to accuse Israel before the Throne of Glory. The gift of the goat forces the Adversary (not unlike Balaam) to utter blessings instead of curses.
(ח) אמר סמאל לפני הקב"ה רבון כל העולמים על כל העכומ"ז נתת לי רשות ועל ישראל אין אתה נותן לי רשות, אמר לו הרי יש לך רשות עליהם ביום הכפורים אם יש להם חטא, ואם לאו אין לך רשות עליהם, לפיכך נותנין לו שוחד ביום הכפורים שלא לבטל את ישראל שלא לבטל קרבן של ישראל, שנאמר "גורל אחד לה' וגורל אחד לעזאזל".
(8) Sammael said before the Holy One, blessed be He: Sovereign of all the universe ! Thou hast given me power over all the nations of the world, but over Israel Thou hast not given me power. He answered him, saying: Behold, thou hast power over them on the Day of Atonement if they have any sin, but if not, thou hast no power over them. Therefore they gave him a present on the Day of Atonement, in order that they should not bring their offering, as it is said, "One lot for the Lord, and the other lot for Azazel" (Lev. 16:8).
You may be asking yourself - what blessings did Samael end up uttering?
Humans are like angels on Yom Kippur
ראה סמאל שלא נמצא בהם חטא ביום הכפורים אמר לפניו רבונו של עולם יש לך עם אחד בארץ כמלאכי השרת בשמים:
מה מלאכי השרת אין להם קפיצין כך ישראל עומדים על רגליהם ביום הכפורים.
מה מלאכי ישראל אין להם אכילה ושתיה כך ישראל אין להם אכילה ושתיה ביום הכפורים.
Sammael saw that sin was not to be found among them on the Day of Atonement. He said before the Holy One, blessed be He: Sovereign of all the universe ! Thou hast one people like the ministering angels who are in heaven. Just as the ministering angels have bare feet, so have the Israelites bare feet on the Day of Atonement. Just as the ministering angels have neither food nor drink, so the Israelites have neither food nor drink on the Day of Atonement. Just as the ministering angels have no joints, in like wise the Israelites stand upon their feet. Just as the ministering angels have peace obtaining amongst them, so the Israelites have peace obtaining amongst them on the Day of Atonement. Just as the ministering angels are innocent of all sin on the Day of Atonement, so are the Israelites innocent of all sin on the Day of Atonement.
There's one other thing we get to do on Yom Kippur because we are like angels: say the second line of the Shema loudly.
(לה) דָּבָר אַחֵר, שְׁמַע יִשְׂרָאֵל. מֵהֵיכָן זָכוּ יִשְׂרָאֵל לִקְרִיאַת שְׁמַע, מִשָּׁעָה שֶׁנָּטָה יַעֲקֹב לְמִיתָה קָרָא לְכָל הַשְּׁבָטִים וְאָמַר לָהֶן שֶׁמָּא מִשֶּׁאֲנִי נִפְטַר מִן הָעוֹלָם אַתֶּם מִשְׁתַּחֲוִים לֵאלוֹהַּ אַחֵר, מִנַּיִן, שֶׁכָּךְ כְּתִיב (בראשית מט, ב): הִקָּבְצוּ וְשִׁמְעוּ בְּנֵי יַעֲקֹב וגו', מַהוּ (בראשית מט, ב): וְשִׁמְעוּ אֶל יִשְׂרָאֵל אֲבִיכֶם, אָמַר לָהֶן, אֵל יִשְׂרָאֵל, אֲבִיכֶם הוּא. אָמְרוּ לוֹ, שְׁמַע יִשְׂרָאֵל ה' אֱלֹהֵינוּ ה' אֶחָד, וְהוּא אוֹמֵר בִּלְחִישָׁה בָּרוּךְ שֵׁם כְּבוֹד מַלְכוּתוֹ לְעוֹלָם וָעֶד. אָמַר רַבִּי לֵוִי וּמַה יִּשְׂרָאֵל אוֹמְרִים עַכְשָׁו, שְׁמַע אָבִינוּ יִשְׂרָאֵל אוֹתוֹ הַדָּבָר שֶׁצִּוִּיתָנוּ נוֹהֵג בָּנוּ ה' אֱלֹהֵינוּ ה' אֶחָד.
When Moses ascended to the supernal abode, he heard the angels singing the words “Baruch shem kevod malchuto le’olam va’ed” (“Blessed be the name of the glory of His Kingdom forever and ever”), and upon his descent he taught it to Israel. Why does Israel not proclaim these words openly [but rather whisper them in an undertone during the daily Shema service]? Says Rabbi Asi, “This is comparable to a man who stole a gem from the royal palace and gave it to his wife. ‘I implore you,’ he said to her, ‘never wear this gem in public, only in the privacy of your home.’ However, on Yom Kippur, when they are pure as angels, they proclaim these words loudly.”
Kapparah: What on earth are you doing with that chicken????
(א) מַה שֶּׁנּוֹהֲגִים לַעֲשׂוֹת כַּפָּרָה בְּעֶרֶב יוֹם כִּפּוּרִים לִשְׁחֹט תַּרְנְגוֹל עַל כָּל בֵּן זָכָר וְלוֹמַר עָלָיו פְּסוּקִים, יֵשׁ לִמְנֹעַ הַמִּנְהָג. הַגָּה: וְיֵשׁ מֵהַגְּאוֹנִים שֶׁכָּתְבוּ מִנְהָג זֶה, וְכֵן כָּתְבוּ אוֹתוֹ רַבִּים מִן הָאַחֲרוֹנִים, וְכֵן נוֹהֲגִין בְּכָל מְדִינוֹת אֵלּוּ וְאֵין לְשַׁנּוֹת, כִּי הוּא מִנְהַג וָתִיקִין.
(1) That which [people] are accustomed to perform kapparah before Yom Kippur by slaughtering a rooster on each male and to say verses over it, you should prevent the custom. Ramah: And there are those from the Geonim that write about this custom, and similarly it is written from many Achronim [Rishonim], and so is the custom in all these countries [Ashkenaz] - and you shouldn't change, for it is an ancient custom.
On Erev Yom Kippur, traditional Jews transfer their sins to a chicken by waving it around their head three times while reciting these words:
"This fowl is my substitute, this is my surrogate, this is my atonement.” Some texts significantly add “May it be designated for death, and I for life.”
The bird was then slaughtered and given to the poor. Some Orthodox Jews have kept this tradition but replace the chicken with a stack of cash, which is then donated to charity.
זה חליפתי, זה תמונתי, זה כפרתי. זה הכסף ילך לצדקה, ואני ואכנס לחיים טובים ארכים ולשלום.
This is in my stead. May this be my substitute; may this be my atonement. This money will go to tz'dakah, that I may enter the path to a good, long life, and to peace.
Kapparah Liturgy from Mahzor Lev Shalem
Omens of the Year to Come
Superstitious Jews came up with numerous ways to divine whether they had been written in the Book of Life or Book of Death for the year to come.
"On the night of Hoshana Rabbah, the seventh day of the Feast of Tabernacles, when it was believed that the decision concerning men's fate during the new year, which had been reached by Yom Kippur, was finally and irrevocably indicted in the celestial book of records, the practice became widespread among medieval Jews to go our into the moonlight and observe whether the shadows they cast were by some ill chance devoid of heads... The colophon of a sixteenth-century manuscript contains these words by the scribe: 'On the night of Hoshana Rabbah, 5315 A.M. [1556 C.E.] I saw the shadow of my head in the moonlight; praised be G-d, for now I am assured that I shall not die on this year.'"
Jewish Magic and Superstition, Joshua Trachtenberg
סר צלם מעליהם מגנם וחזקם כשרים שבהם מתו דבר אחר צלו של מקום סר מעליהם לשון רש"י (רש"י על במדבר י״ד:ט׳) ורבי אברהם אמר כי צלם מגן וצנה אשר הם צל על הנלחמים יאמרו כי נפל פחדנו עליהם ולא יקחו מגן וצנה וכובע להחלץ להלחם כנגדנו ויפה פירש אבל יתכן שירמוז הכתוב למה שנודע כי בליל החותם לא יהיה צל לראש האיש אשר ימות בשנה ההיא לכך יאמר כבר סר צלם מעליהם שנגזר עליהם מיתה וה' אתנו כי הוא השוכן בקרבנו ועושה לנו נסים ונפלאות לעיני כל רואה
TZILAM’ (literally: “their shadow”) IS REMOVED FROM THEM. “That is, their shield and their strength [are departed from them]. The worthy ones among them have died. Another interpretation: the shade (protection) of G-d is departed from them.” This is Rashi’s language...
But it is possible that Scripture is alluding to the well-known fact that there will be no shadow over the head of a person who is [destined] to die that year, on “the night of the seal.” Therefore it says: “their ‘shade’ is already removed from them, meaning that death has been decreed upon them, and the Eternal is with us, for it is He Who dwells in our midst and does miracles and wonders for us in the eyes of all who behold us; therefore, fear them not.”