(כד) דַּבֵּר אֶל בְּנֵי יִשְׂרָאֵל לֵאמֹר בַּחֹדֶשׁ הַשְּׁבִיעִי בְּאֶחָד לַחֹדֶשׁ יִהְיֶה לָכֶם שַׁבָּתוֹן זִכְרוֹן תְּרוּעָה מִקְרָא קֹדֶשׁ. (כה) כָּל מְלֶאכֶת עֲבֹדָה לֹא תַעֲשׂוּ וְהִקְרַבְתֶּם אִשֶּׁה לַיהוָה.
(24) Speak unto the children of Israel, saying: In the seventh month, in the first day of the month, shall be a solemn rest unto you, a memorial proclaimed with the blast of horns, a holy convocation. (25) You will do no manner of servile work; and you will bring an offering made by fire unto the LORD.
(א) וּבַחֹדֶשׁ הַשְּׁבִיעִי בְּאֶחָד לַחֹדֶשׁ מִקְרָא קֹדֶשׁ יִהְיֶה לָכֶם כָּל מְלֶאכֶת עֲבֹדָה לֹא תַעֲשׂוּ יוֹם תְּרוּעָה יִהְיֶה לָכֶם.
(1) And in the seventh month, on the first day of the month, you will have a holy convocation: you will do no manner of servile work; it is a day of blowing the horn unto you.
אמר רבי אבהו למה תוקעין בשופר של איל אמר הקדוש ברוך הוא תקעו לפני בשופר של איל כדי שאזכור לכם עקידת יצחק בן אברהם ומעלה אני עליכם כאילו עקדתם עצמכם לפני
In the Talmud in the section about Rosh HaShannah we learn:
Rabbi Abihu said: Why do we blow on a ram's horn? The Holy One, Blessed be G-d, said: Sound before Me a ram's horn so that I may remember on your behalf the binding of Isaac, the son of Abraham, and account it to you as if you had been bound yourselves before Me.
The Baal Shem Tov, Keter Shem Tov, 194
A King had a son, an only child. The King wanted his son to learn and to experience various cultures, so he sent him to a far-off country, supplied with a generous quantity of silver and gold. Far away from home, the son carelessly spent all the money until he was left completely destitute. In his distress he resolved to return to his father's house and after much difficulty, he managed to arrive at the gate of the courtyard to his father's palace.
He had forgotten the language of his native country, and he was unable to identify himself to the guards. In utter despair he began to cry out in a loud voice, and the King, who recognized the voice of his son, went out to him and brought him into the house, kissing him and hugging him.
The meaning of the parable: The King is G-d. The prince is the Jewish people, who are called "Children of G-d" (Deuteronomy 14:1). The King sends a soul down to this world in order to fulfill the Torah and mitzvot. However, the soul becomes very distant and forgets everything to which it was accustomed to above, and in its exile it forgets even its own "language." So it utters a simple cry to G-d in Heaven. This is the blowing of the shofar, a cry from deep within, expressing regret for the past and determination for the future. This cry elicits G-d’s mercies, and G-d demonstrates God's abiding affection for G-d's children and G-d forgives them.