Atonement is the spiritual process by which God provided a means to satisfy the need for a penalty for human sin while still extending mercy to all people. Christ's voluntary sacrifice reconciled the need for both justice and mercy. Justice says that sinners should be executed for violating the Eternal's holy laws (cf. Romans 5:12; 4:15).
Mercy says that sinners have to be excused from the penalty of the law if they are to be reconciled to him (Romans 5:8 - 11). Atonement reconciles these two characteristics of God's perfect nature.
Christ's sacrifice ensures that no man or woman has to die forever for his or her disobedience since He paid the penalty in his or her stead. So, when did Jesus complete his atonement for us all? His atoning work took place not only when he died but also when he was resurrected from the dead. This work will only ultimately become effective in individual lives when people repent and have faith in His sacrifice.
It is important to note the atonement made possible by Jesus' death and resurrection to life were both necessary so we could be made right with God. The Messiah's death paid the penalty for sin, but his life ensures that we will be resurrected to eternal life. We have to have eternal life in order to be reconciled and to have a continuing living relationship with the Father for all eternity. The fifth chapter of Romans states Christ had to die AND come back to life in order to save us (Romans 5:9 - 10).
A key text that proves Jesus' sacrifice was necessary for the forgiveness of our sins is located in Romans 3. It states, "[Believing sinners] being justified as a gift by His grace through the redemption which is in Christ Jesus; whom God displayed publicly as a propitiation in His blood through faith . . . that He might be just and the justifier of the one who has faith in Jesus (Romans 3:24 - 26, NASB).
The NIV translation uses "sacrifice of atonement" in place of "propitiation" in verse 25 of Romans 3. In this case, God provides a sacrifice for mankind, instead of man providing one, in order to restore the relationship that existed before sin. Adam and Eve's disobedience cut off the human race from their Creator. Since then we have all been born into a sinful, fallen world, and have sinned ourselves (Romans 5:12).
There is, however, a bigger picture that must be considered when we analyze what does atonement mean and the Old Testament Holy day that centers around its fulfillment (commonly called Yom Kippur, Leviticus 16, 23:26 - 32, Numbers 29:7 - 11).
The atoning is only effectively applied to the whole world when it repents and is no longer influenced by Satan, who is represented by the Azazel goat sent into the wilderness (Leviticus 16:8, 10, 20 - 22, 26). This goat represents God holding the devil responsible for his part in actively deceiving all humans to sin.
Just as physical Israel depended on the high priest to make atonement for his nation on Yom Kippur, the world will depend on Jesus as high priest and as coming King to effectively atone for its sins by removing Satan and establishing His kingdom on earth (See Revelation 5:10, 11:15, 20:1 - 4). Therefore, the general application of his sacrifice will only occur after His return. Until then, only a relatively few true Christians will receive the full benefits of his sacrifice (cf. John 6:44, 65, Matthew 13:11 - 16).