[<< wikibooks] Hebrew Roots/Holy Days/Day of Atonement/Atonement/Overview
The Day of Atonement or Yom Kippur, as it is in Hebrew, rather than being a feast day is really a day of fasting.
Yom Kippur  (Leviticus 23:27; 25:9)  is called the Day of Atonement, the Day of Judgment, the Sabbath of Sabbaths, the Day of Redemption, the Day of the Fast or the Great Fast (Acts 27:9.5).

The Greek translation of the Old Testament, known as the Septuagint, calls it hemera exilasmou, that is, "the Day of Expiation."
The same rendering is found in the Latin Vulgate, 'dies expiationum' the"Day of Expiation" or "Propitiation."  Kippur in Hebrew means 'to pardon', or 'condone'. The word 'atonement' carries the same meaning in our language. It means to make amends or to reconcile - to become "at one."Yom Kippur occurs on the tenth day of Tishri the seventh month in the Hebrew calendar and is the most solemn day in the whole religious year. The work of redemption was initiated on Passover and completed at Yom Kippur, where the final atonement and judgment of sin is made effective. It is significant that the cleansing of the Day of Atonement is preceded by the repentance of the Feast of Trumpets and is followed by the rejoicing of the Feast of Tabernacles. The spiritual lesson is evident. The children of Israel could only rejoice after they had repented of their sins and experienced the cleansing and renewal of redemption. 
Yahweh’s order can be seen in the end of year feasts:- 

Yom Teruah (Rosh Hashanah) is the time of repentance
Yom Kippur brings forgiveness and reconciliation
Sukkot brings joy and blessings

The daily, weekly, and monthly sacrifices made at the altar of burnt offering were not sufficient to atone for sin and even at the altar of burnt offering the worshiper stood “afar off,” unable to approach the Holy Presence of Yahweh God, who was manifest between the cherubim in the Holy of Holies.   On this one day in the year, atoning blood was brought into the Holy of Holies, representing the divine throne room, by the High Priest.  He stood as the representative of the people to make reconciliation for the priesthood and the people and to purify the sanctuary itself from the sins confessed there during the year, thus also cleansing the temple.  His ministry consisted of --											
(1) the purification of himself, the sanctuary, the priesthood, and the people :(Leviticus 16:16-19, 30, 33, 34)   
(2) the expulsion of Azazel, which bore the judgment of the people's sins :(Leviticus 16:10, 20-22)
The High priest took a sin-offering for himself and for his house before he commenced the work of atonement for the people. He then took two goats, one for Yahweh and one for 'Azazel'. The goat for Yahweh was sacrificed to make atonement for the sins of the people which had already been confessed throughout the year. All of the sacrifices for sins offered throughout the year were intended to atone for the individual personally ("The priest shall make atonement for him, and he shall be forgiven" [Lev 4:31,35; 5:6,10, 13;12:6-8]), but not for the sanctuary.
The rites performed on that day concluded the atoning process of the sins of the Israelites by removing them permanently from the sanctuary itself. The cleansing was accomplished by the High Priest sprinkling the blood seven times first upon the mercy seat in the most Holy Place, and then upon the altar of burnt offering in the court. "Thus he shall make atonement for the holy place, because of the uncleanness of the people of Israel, and because of their transgressions, all their sins" (Leviticus 16:16). The altar of burnt offerings was also sprinkled with blood seven times in order to "cleanse it and hallow it from the uncleanness of the people of Israel" (Leviticus 16:19).
The record of forgiven sins was kept in the sanctuary until the Day of atonement because such sins were to be reviewed by the heavenly court during the final judgment typified by the Feast of Trumpets, and also to provide a last opportunity to God’s people to review their own lives before Yom Kippur and repent of any sins which had not been forsaken previously. Thus, the sins of the people, from which the sanctuary had been cleansed through oral confession, were transferred by the laying on of hands to the live goat which was sent away into the wilderness for its elimination from the Israelite community. (Leviticus 16:10, 21). It was taken by escort to a  designated precipice and a red sash attached to the head of the goat was tied to a protrusion on the cliff. Then the goat would be pushed over the cliff, sending him to his death together with Israel’s sins. A portion of the crimson sash that was tied around its head was attached to the door of the Temple before the goat was sent into the wilderness. When the goat met its death, the sash attached to the Temple’s door would turn white signifying that the sins of Israel had been forgiven.   (After Messiah's sacrifice, the sash no longer changed from red to white  [Isaiah 1:18] Yoma 68b).

Y'shua's work of atonement fulfilled what was foreshadowed in the rites of Yom Kippur. He was the "goat for Yahweh" which was sacrificed for the sins of the people. He died on the tree as a substitute for us and took the retribution for our sins against God (Mark 10:45; 1 Timothy 2:5-6; 1 Corinthians 6:20; 7:23).  The ransom price of blood was thirty pieces of silver and the shedding of blood made an atonement for sin (Leviticus 17:11; Romans 5:8-11). 
Y'shua "put away sin by the sacrifice of Himself" (Hebrews 9:26) and with His entrance into the presence of God "a new and living way" (Hebrews 10:20) of access to God was opened for mankind. The veil which separated the inner sanctuary from the people was torn in two from the top to the bottom in a divine act of God when Y'shua, acting as our High Priest, "entered the Most Holy place once for all, having obtained eternal redemption"  -  "not with the blood of bulls or goats, but with His own blood" (Hebrews 9:12). By  Messiah's access into the presence of God, believers now can "enter into the inner sanctuary behind the curtain" (Hebrews 6:19) and have direct access into the presence of God.  
He made one sacrifice for all time and for the forty years after the sacrifice of Y'shua, until the destruction of the temple, Yahweh no longer accepted the sacrifice of the High Priest for the people on Yom Kippur. Whereas the scarlet sash attached to the scapegoat had always turned white when the sacrifice was accepted, it ceased to do so after Y'shua's atonement for sin from 30 AD onwards. The old system of atonement was superseded by the new.
The goat for Azazel (the "scapegoat") symbolized the condemnation of Satan for the sins of all humanity and fulfills the type of Satan being sent to the abyss   (Revelation 20:1-3, 7-10).
AND yah should live forever because he is our saver and soon coming king

The book of Hebrews recognizes a past, present, and a future aspect in Messiah's redemptive work represented in the Day of Atonement. In the past, Messiah "appeared once for all at the end of the age to put away sin by the sacrifice of himself" (9:26). In the present ("now"), Messiah "appears in the presence of God on our behalf" (9:24). In the future, Messiah "will appear a second time, not to deal with sin but to save those who are eagerly waiting for him" (9:28). 
The present and the future ministry of Messiah were all effected by His atoning sacrifice that enables Him to fulfill the two phases of His ministry in the heavenly sanctuary of  intercession for us now and judgment soon to come.
The Day of Atonement typifies the consummation of Messiah’s redemptive ministry at His Second Advent, when He will dispose of sin by saving true believers and punishing the unbelievers. Just as the confessed and forgiven sins of the Israelites were retained in the sanctuary until their final disposition on Yom Kippur, so the confessed and forgiven sins of believers today are recorded in the heavenly books where they remain until their final disposition on the Day of Messiah’s coming. Although sins are forgiven, they are not disposed of from the temple which is His Body, until His return.  (Romans 8:20-23)
The sending of the azazel goat out into the wilderness as done by the Old Testament high priest after he returned from inside The Most Holy Place of the Tabernacle, represents the permanent removal and elimination of sin and of Satan who will ultimately bear responsibility for all the sins and evil he instigated, and is a ceremonial "preview" of Messiah pronouncing the final guilty verdict upon Satan as the source of all evil, and the sentencing of him to the abyss which will cleanse the heavenly sanctuary (Revelation 20: 1-3; 10). Thus Satan (Azazel) will bear the judgement for all the sins he has instigated as well as upon those who have followed him in rebellion against God and have not forsaken their sins and received the atonement.
There will be a separation of true and false believers, sheep and goats. The sheep are the true believers and the goats are those who identify with the "Goat" (Azazel), the symbol of Satan.
On this Day, there remains ‘no further sacrifice for sin’ for those who ‘deliberately keep sinning,’ ‘but only a fearful expectation of judgment and a flaming fire to consume the adversaries of God’ (Hebrews 10:25-31; cf. Leviticus 23:29-30).
Evildoers in the kingdom, the tares, will be thrown "into the furnace of fire," and the "righteous will shire like the sun in the kingdom of their Father"   Y'shua compared this separation to the one that takes place at harvest time between the wheat and the tares.   The tares were sown among the good wheat which represents "the sons of the kingdom."  Wheat and tares, genuine and false believers will co-exist until His coming. At that time the drastic separation typified by the Day of atonement will occur. (Matthew 13:38, 42-43). This will be the complete eradication of sin and sinners, the binding and ultimate judgment of Satan, and the establishment of a new world which are all typified by the ritual of the Day of atonement. This will complete the work of redemption which began at the crucifixion.

Although all of the feasts have had a historic fulfillment there remains a spiritual reality to be rehearsed each year as we commemorate the spiritual truths resident in the typology of them.
For us personally, the Day of Atonement represents the completion of the work of the atonement in our own lives which began at salvation (which relates to Passover).   There is a spiritual progression through of sanctification typified in the Feast of Unleavened Bread, on to betrothal to Messiah at Pentecost, then coming to the seventh month which typifies maturity and perfection with repentance and cleansing for all sin at the Feast of Trumpets.
As we seek complete "at-one-ment" with our heavenly Father in full appropriation of the work of the crucifixion in our lives each year, we are rehearsing and preparing for the final conclusion of the ages.
The Day of the Atonement prophetically, is for the purification of the Bride.  The Feast of Tabernacles which follows is a prophetic picture of the Marriage Feast of the Lamb and Shemini Atzeret (Eighth Day Assembly) represents us dwelling with Him for ever.   John 14:1-3
An incidental reference to Yom Kippur is found in Acts 27:9 in the context of Luke’s description of Paul’s perilous voyage to Rome. Translators and commentators agree that "the Fast" mentioned by Luke in Acts 27:9 is the Day of Atonement because, the day was commonly called "the Fast." Some versions, like the NIV, provide this marginal explanation, "that is, the Day of Atonement (Yom Kippur)". As seen by other references, Paul kept these feasts with the believers (Acts 18:21; 12: 3; 20:6) who kept Yom Kippur as part of the new covenant observances.
Yahweh said to Moses, "Also the tenth day of this seventh month is the Day of Atonement. It shall be a holy convocation for you; you shall afflict your souls, and make an offering made to Yahweh by fire.   And you shall do no work on that day, for it is the Day of Atonement, to make atonement for you before Yahweh your God.   For any person who is not afflicted in soul on that same day shall be cut off from his people.   And any person who does any work on that same day, that person I will destroy from among his people. You shall do no manner of work;  it shall be a statute forever throughout your generations in all your dwellings. It shall be a Sabbath of solemn rest, and you shall afflict your souls;   On the ninth day of the month at evening, from evening to evening; you shall celebrate your Sabbath."    Leviticus 23:26-32
This is a Sabbath of Sabbaths, the holiest Sabbath of the year, to be set aside completely for seeking Yahweh.  A "day of solemn rest" from all else and a day to "afflict your souls", which is understood to be in fasting - abstinence from all forms of physical pleasure and bodily appetites.  Fasting heightens our awareness of spiritual needs and helps to bring the body and it's desires under subjection.  A complete fast may not be possible for the elderly, those with physical problems, pregnant women and children, but the principle should be implemented, as able.
Psalm 35:13  connects fasting with humbling oneself, and the same idea is seen in Isaiah 58: 3.   Most important is our heart attitude in what we do,  rather than merely the act of fasting -   Isaiah 58:6. If we come in humility and repentance He will hear our cry on Yom Kippur for cleansing -   Isaiah 58:9  
With the cessation of the sacrificial system,  personal prayer and repentance became the offerings that substituted the sacrificial offerings made to Yahweh on that day. (Psalm 141: 2) 
A mikveh (ritual immersion in water) is taken before the commencement of the day as part of the spiritual cleansing and white is worn to symbolize the cleansing and purity offered by Yahweh on that day.
The confession of sins is the high point of Yom Kippur, and the Jewish tradition is to confess sin in the plural form , "we have sinned".  The reason is that "we must share the guilt of another’s transgression because of our lack of effort in preventing others from straying." S. M. Lehrman (note 62), p.195.    
This is part of loving our neighbour as ourselves.
Everyone confesses all sins, and each individual applies the appropriate category to himself or herself.    The focus is not just of the sins of society, but on the changes needed in one’s personal life. 
"People dredge up their sins, but in a way they are glad to do so because the sins remembered and repented of, are all forgiven. . . . Thus, Yom Kippur is both a fierce jolt and a great relief." (Irving Greenberg (note 2), p. 212). 
The final service of Yom Kippur is the "Neilah".  It is the Jewish belief that the gates of Heaven are open during the "Days of Awe" (from Yom Teruah to Yom Kippur) to receive our prayers for forgiveness and that they close after this last service with the final blast of the shofar (the Shofar HaGadol, the Great Trumpet).  Those who have observed the day with sincerity will have been inscribed and sealed in the Book of Life.  On a future Yom Kippur the sealing of His servants will mean their preservation from the end-time judgment upon the ungodly.   Revelation 7: 2-3