The Day of Atonement, or Yom Kippur as it called in Hebrew, is one of the seven yearly times that God has appointed for His people and laid out for us in Leviticus chapter 23.
This day is the second of the fall appointed times and is solemn day of affliction, humility, repentance, and remembrance of the cost of sin. It's placement between the day of trumpets and feast of tabernacles, and it solemn and holy nature, lead many to believe that it prophetically points to the day of judgment. Which scripturally comes after the final trumpet has sounded and the dead are raised, but before Christ's millennial kingdom.