The biblical text describes the sacred occasion as one commemorated with loud blasts, and gives us two key mitzvot, one positive and one negative, in observing the solemn occasion. The positive one is to observe complete rest. The negative one is to refrain from doing labor.
The day is to be commemorated with loud blasts. Rashi clarifies the meaning of the loud blasts:
In the biblical text, the loud blasts are written as "zicharon t'ruah". Rashi aligns the "zicharon"--loud--with remembrance, linking it with the remembrance of the Akeidah - the Binding of Isaac, in whose stead a ram was provided, caught by his horn in the bushes.
Rashi then refers to a Talmudic passage in Rosh Hashana 32a, which links 3 themes together: blessings of kingship, remembrance, and shofarot. The concept of kingship occurs in the Biblical verse preceding our passage, Lev 23:22, "I am the LORD Your God". The concept of remembrance equates with the blasts of the shofarot, which make this a sacred occasion, which is observed by the prohibition against labor.
Mishneh Torah further clarifies that the yovel, the ram's horn that is blown, is a bent horn. All others are excluded. Furthermore, even though the actual word shofar is not specifically mentioned in the Biblical text, it is later used in the passage relating to the Jubilee year. Oral tradition links the 2 together, clarifying that the loud blasts for Rosh Hashana must be made with a bent ram's horn, aka shofar.
(א) מִצְוַת עֲשֵׂה שֶׁל תּוֹרָה לִשְׁמֹעַ תְּרוּעַת הַשּׁוֹפָר בְּרֹאשׁ הַשָּׁנָה שֶׁנֶּאֱמַר (במדבר כט א) "יוֹם תְּרוּעָה יִהְיֶה לָכֶם". וְשׁוֹפָר שֶׁתּוֹקְעִין בּוֹ בֵּין בְּרֹאשׁ הַשָּׁנָה בֵּין בְּיוֹבֵל הוּא קֶרֶן הַכְּבָשִׂים הַכָּפוּף. וְכָל הַשּׁוֹפָרוֹת פְּסוּלִין חוּץ מִקֶּרֶן הַכֶּבֶשׂ. וְאַף עַל פִּי שֶׁלֹּא נִתְפָּרֵשׁ בַּתּוֹרָה תְּרוּעָה בְּשׁוֹפָר בְּרֹאשׁ הַשָּׁנָה הֲרֵי הוּא אוֹמֵר בְּיוֹבֵל (ויקרא כה ט) "וְהַעֲבַרְתָּ שׁוֹפַר" וְכוּ' (ויקרא כה ט) "תַּעֲבִירוּ שׁוֹפָר". וּמִפִּי הַשְּׁמוּעָה לָמְדוּ מַה תְּרוּעַת יוֹבֵל בְּשׁוֹפָר אַף תְּרוּעַת רֹאשׁ הַשָּׁנָה בְּשׁוֹפָר:
(1) It is a positive commandment from the Torah to hear the sound of the shofar (animal horn) on Rosh Hashanah; as it is stated (Numbers 29:1), "it shall be a day of blowing for you." The shofar which is blown — both on Rosh Hashanah and for the Jubilee year — is a bent ram's horn. And all shofars are disqualified except for the horn of a ram. Even though blowing with a shofar is not mentioned explicitly [in the passage] about Rosh Hashanah; it surely does state about the Jubilee year (Leviticus 25:9), "you shall blast the shofar." And we have learned through the oral tradition that just as the blowing of the Jubilee year is with a shofar, so too is the blowing of Rosh Hashanah with a shofar.
What does all of this teach us? The loud blasts--blowing of the Shofar--are so important that the definition of the shofar is critical; only one kind of horn (yovel) will suffice. Furthermore, hearing the blowing of the shofar is a critical part of this solemn occasion of rest. It is so important that not only must we hear it, but we must also listen to it. Just as we recite "Shema Yisrael..."--hear and listen simultaneously--we must actively internalize the sound of the blasts and what they mean to us: remembrance; a remembrance that is so important we are commanded to observe an entire day of sacred rest while we absorb and remember. We will shortly read the narrative of the Akeidah from the Sefer Torah, which we are instructed to remember. However, your task in remembering is to understand what the Akeidah means to you--whether it's a statement of theology, or of redemption, or of our heritage.