Day of Atonement
The Day of Atonement is on the 10th of Tishri and is the most holy day of the year. This is the only day the High Priest enters the temple's Holy Place. He sacrifices an ram, bull and goat then sprinkles the blood on the Ark of the Covenant. This is a day of national repentance and forgiveness for the sins of Israel. The Jewish people observe a twenty-five hour fast of food and water.
I [God] will pour upon the house of David, and upon the inhabitants of Jerusalem, the spirit of grace and of supplications: and they shall look upon me whom they have pierced, and they shall mourn for him, as one mourns for his only son, and shall be in bitterness for him, as one that is in bitterness for his firstborn (Zechariah 12:10).
Feast of Tabernacles
The Feast of Tabernacles is from the 15th to the 21st of Tishri. It is a joyous celebration of the presence of God. On Tabernacles, the first Jewish temple was dedicated by Solomon and the Spirit of God entered the temple. Jesus Christ was conceived on Hanukkah but was born on Tabernacles. God the Father dwelt in the tabernacle and temple, God the Son dwelt with humanity as a man and during the future Millennium as God, so God the Holy Spirit dwells within Christians. During Tabernacles, the people live in booths. On the first day of Tabernacles 2015, there will be a "blood moon" and fourth lunar eclipse on a holy day in a row.
Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God (Revelation 21:3).