The Meaning of It
In my place, for my sins, on the cross, He died. Vicarious substitutionary atonement.
The Accomplishment of It
Redemption
Redemption Results
Propitiation (God-ward)
The satisfaction of divine justice
Propitiation Results
God is Justified in Forgiving Sin (acting justly)
Now God is Justified in Bestowing Righteousness
Reconciliation (Man-ward)
Restoration to favor.
Reconciliation Results
New creatures in Christ (2 Corinthians 5:17)
The Extent of It
The view of limited atonement.
The view of unlimited atonement.
The agreement between atonement views.
Christ's death is sufficient to save all men if God should chose so to do.
The actual application of Christ's satisfaction is clearly not to everybody, for some perish.
A sincere universal offer of salvation on the condition of faith is made in the Bible.
All who sincerely come to Christ will find the atonement has been made for them.
Application
This is a work of the Holy Spirit whether in evangelism or in Christian life application.