The most important Mitzva of Rosh haShana is listening to the Shofar. The Tora does not mention the reasons for the Shofar. But our Rabbis did.
1. The Shofar was used in ancient Israel to announce the King's coronation. In Rosh haShana we announce that God is our King ('ol malkhut shamayim). We are His subjects and as such we follow His rules. Among other prerogatives the King had the power to sentence to death or spare someone's life. In Rosh haShana we realize that our lives are ultimately in the hands of God, the supreme King and Judge. The key word which is added and emphasized in the prayers of Rosh HaShana and Yamim Noraim is melekh (=King). God is the King and Supreme Judge. He decides who lives and who does not.
2. The Shofar also reminds us of aqedat Yitzhaq. Abraham Abinu was ready to sacrifice his own son, following God's commandment. Once Abraham showed his unconditional obedience and love to God, God told him to hold back. Abraham saw a ram caught by its horns in a thicket and he offered it as a sacrifice to Him instead of Ytzhaq. The Shofar is a ram's horn.
3. In ancient times, the Shofar was also used as a kind of a siren. It warned the people when the enemy was approaching and about to attack. The Shofar announced that lives were in danger. In Rosh haShana the Shofar serves as a spiritual wake up call. Reminding us the fragility of our lives and inviting us to introspect and repent. The Shofar remind us that God is NOW judging us and our lives are on the line.
In Hilkhot Teshuba 3:4 Maimonides explains that when listening to the Shofar we should hear the following message: "Wake up, sleepy ones. And those who slumber, arise! Inspect your deeds. Remember your Creator. Those who forget the truth because of the temporary distractions and throughout the entire year, devoting their strength to the pursue of vanity and material emptiness which will not benefit, not save. Examine your ways and your deeds. Abandon the paths of evil. And stay away from destructive habits and negative thoughts."
A modern narrative of 'aqedat Ytzhaq