Rosh Hashanah (also known as the head of the year) is celebrated as New Years Day. It occurs on the first two days of the Hebrew month of Tishri, September/October time, and marks the beginning of a ten-day period of prayer, self-examination and repentance, which culminates on the fast day of Yom Kippur.
Day of Atonement
Yom Kippur, or the Day of Atonement, is the holiest day of the Jewish year, and provides prophetic insight regarding the Second Coming of Mashiach, the restoration of national Israel, and the final judgment of the world. It's also a day that reveals the High-Priestly work of Yeshua as our Kohen Gadol1 after the order of Malki-Tzedek (Hebrews 5:10, 6:20)
The term Yom Kippur is actually written in the plural in the Torah, Yom Ha-Kippurim, perhaps because the purification process cleansed from a multitude of transgressions, iniquities, and sins. However, the name also alludes to the two great atonements given by the LORD — the first for those among the nations who turn to Yeshua for cleansing and forgiveness, and the second for the purification of ethnic Israel during Yom Adonai, the great Day of the LORD at the end of days.
Kippurim can be read as Yom Ke-Purim, a day like Purim, that is, a day of deliverance and salvation2. Thus the day on which Yeshua sacrificed Himself on the cross is the greatest Purim of all, since through Him we are eternally delivered from the hands of our enemies.
The Torah states that Yom Kippur was the only time when the High Priest could enter the Holy of Holies and call upon the Name of YHVH to offer blood sacrifice for the sins of the people. This life for a life principle is the foundation of the sacrificial system and marked the great day of intercession made by the High Priest on behalf of Israel.
Days of Awe
In traditional Judaism, the day of Yom Kippur marks the climax of the ten day period of repentance called the Days of Awe, or yamim nora’im. According to the sages of Jewish tradition, on Rosh Hashanah the destiny of the righteous, the tzaddikim, are written in the Book of Life, and the destiny of the wicked, the resha’im, are written in the Book of Death. However, most people will not be inscribed in either book, but have ten days — until Yom Kippur — to repent before sealing their fate. Hence the term Aseret Yemei Teshuvah — the Ten Days of Repentance. On Yom Kippur, then, every soul’s name will be sealed in one of the two books, for this reason it is really the climax of the 40 day Season of Teshuvah.