Also on the tenth day of this seventh month there shall be a day of atonement ... and ye shall afflict your souls, and offer an offering made by fire unto the Lord. (Lev. 23:27.)

Yom Kippur is the day of atonement for the Jewish people. It is considered one of the holiest days of the year. It's a day of repentance of sins committed against God. The day should be spent concentrated on prayer, repentance, and self-improvement before returning to the usual daily routine after the holiday. It is celebrated in September or October. Many Jews wear white and fast on this day. They often stay home from work and observe several prayers throughout the day.

Here are some great articles:

Symbols of the Harvest: Old Testament Holy Days and the Lord's Ministry from LDS.org

By Lenet H. Read

"Anciently, it was on this day that the high priest would enter the Holy of Holies and there give an offering of blood that would atone for the sins of Israel, reuniting Israel with God. It was on this day that the ritual of the scapegoat was performed, where Aaron symbolically transferred all the sins of Israel upon the head of a goat.

"Christ performed the act of atonement in the meridian of time. But the majority of Judah rejected the atonement. We know that in the last days there will be a refining by affliction of all mankind, with the nation of Israel a central figure in that refinement preparatory to their acceptance of Christ*s atoning work. Christ gives this description of those days:

"For then shall be great tribulation, such as was not since the beginning of the world to this time, no, nor ever shall be.

"And except those days should be shortened, there should no flesh be saved." (Matt. 24:21-22.")

Symbols of the Harvest: Old Testament Holy Days and theLord's Ministry from LDS.org

The scapegoat on the day of Atonement

From the Seminary New Testament Manual, 2016, Lesson 32

The law of Moses provided a foreshadowing of Barabbas’s release centuries before it happened. The law of Moses taught that once a year, on the Day of Atonement, the high priest selected two goats. One goat became the scapegoat and was released alive into the wilderness, while the other was ‘for the Lord’ and was killed as an offering for the sins of the people (seeLeviticus 16:8–10). The high priest then took blood from the slain goat into the Holy of Holies of the tabernacle. He sprinkled it on the lid of the ark of the covenant (called the mercy seat), symbolically making atonement for the sins of Israel.

Gerald N. Lund, who later became a member of the Seventy, explained how the events on the Day of Atonement foreshadowed the Savior’s offering of His blood: “Christ, as the lamb of Jehovah as well as High Priest, shed his own blood to enter the heavenly Holy of Holies where that blood ransomed from their sins those who would believe in him and obey his commandments. (See Heb. 9:11–14, 24–28; 10:11–22; D&C 45:3–5.)” (Jesus Christ, Key to the Plan of Salvation [1991], 67).

Yom Kippur: When is the Jewish Day of Atonement and what is it about? in the International Business Times

I showed the video Ya'ale Tahanunenu - Yom Kippur. It's about a man who looks into a mirror and marks his good deeds and his bad deeds. Then he washes the mirror in a river for atonement. It went well with this quote by President Dieter F. Uchtdorf of the First Presidency:

I printed out the smaller version and added a small circular 1" mirror that I got in the craft department at JoAnn's. I placed the mirror in the center of the circle.

The students placed the quote in their journals.

The day went well. I wore white and gave them a short explanation of the Jewish traditions. I was able to continue with a lesson on the Atonement out of the Doctrinal Mastery New Testament Manual.