For generations, Rosh ha-Shanah, the New Year festival, and Yom Kippur, the Day of Atonement, have been called the Days of Awe.
The word "awe" is used here, as in numerous places in the Bible, to express a sense of the sublime, which generates feelings of reverence for God's majesty.
Our Patriarch Jacob, in describing the place where he had his vision of the ladder to Heaven, says, "How awesome is this place! This is none other than the house of God, and this is the gate of Heaven" (Genesis 28:17).
The word is also mentioned in the Writings, "God is of awesome majesty" (Job 37:22), and in the Song of the Sea, after the miraculous parting of the Red Sea, "Who is like unto You … awesome in praises, doing wonders?" (Exodus 15:11).
Though Rosh ha-Shanah and Yom Kippur differ from each other in liturgy and law, and even in their character and content, they do share many common aspects.
Unlike other festival days, which are times of joy and commemoration of the miraculous deeds and gracious favor bestowed on the nation of Israel since its beginning, the Days of Awe are related to the essential nature of man in the present, to his private life and immediate concerns.
The Days of Awe are not associated with historical events or agricultural production.
On these days, each Jew stands alone, though within a congregation, among other people–facing the Creator.
On the Days of Awe, one must stand before the Lord God, before the Divine throne of judgment, the seat of justice and mercy.
Throughout all the emotional changes that occur during these days, the one constant feeling is the awareness of standing before the "King, Lord of Hosts" (Isaiah 6:5), "the great, mighty, and awesome" (Deuteronomy 10:17).
–Rabbi Adin Steinsaltz
From A Guide to Jewish Prayer by Rabbi Adin Steinsaltz