“Propitiation means the turning away of wrath by an offering. In relation to [salvation], propitiation means satisfying the wrath of God by the atoning sacrifice of Christ.” 
Jesus removes God’s wrath from us by receiving God’s wrath on Himself.
“The word propitiation carries the basic idea of appeasement, or satisfaction, specifically towards God. Propitiation is a two-part act that involves:
- Appeasing the wrath of an offended person
- Being reconciled to them.
Propitiation is that by which it becomes consistent with God’s character and government to pardon and bless the sinner. Propitiation does not procure God’s love or make God loving; it only renders it consistent for God to exercise his love towards sinners.”
In 1 John 2:2; 4:10, Christ is called the “propitiation for our sins.” Here a different Greek word is used, hilasmos. Christ is “the propitiation,” because by his becoming our substitute and assuming our obligations He expiated (atoned for wrongdoing) our guilt, covering it by the vicarious punishment which he endured.
Propitiation vs. Expiation
Propitiation literally means to make favorable and specifically includes the idea of dealing with God’s wrath against sinners. Expiation literally means to make pious and implies either the removal or cleansing of sin.
The idea of propitiation includes that of expiation as its means; but the word “expiation” has no reference to quenching God’s righteous anger. The difference is that the object of expiation is sin, not God. One propitiates a person, and one expiates a problem. Christ’s death was therefore both an expiation and a propitiation. By expiating (removing the problem of) sin God was made propitious (favorable) to us.
ESV Study Bible on Propitiation in Romans 3:25
“Jesus’ blood ‘propitiated’ or satisfied God’s wrath (1:18), so that his holiness was not compromised in forgiving sinners. Some scholars have argued that the word propitiation should be translated expiation (the wiping away of sin), but the word cannot be restricted to the wiping away of sins as it also refers to the satisfaction or appeasement of God’s wrath, turning it to favor (cf. note on John 18:11). God’s righteous anger needed to be appeased before sin could be forgiven, and God in his love sent his Son (who offered himself willingly) to satisfy God’s holy anger against sin. In this way God demonstrated his righteousness, which here refers particularly to his holiness and justice. God’s justice was called into question because in his patience he had overlooked former sins. In other words, how could God as the utterly Holy One tolerate human sin without inflicting full punishment on human beings immediately? Paul’s answer is that God looked forward to the cross of Christ where the full payment for the guilt of sin would be made, where Christ would die in the place of sinners. In the OT, propitiation (or the complete satisfaction of the wrath of God) is symbolically foreshadowed in several incidents: e.g., Ex. 32:11–14; Num. 25:8, 11; Josh. 7:25–26.” 
 Charles C. Ryrie (1999-01-11). Basic Theology: A Popular Systematic Guide to Understanding Biblical Truth(Kindle Locations 5503-5504). Moody Publishers. Kindle Edition.
 Easton’s Bible Dictionary, 3rd edition, 1897 (public domain).
 Crossway Bibles (2009-04-09). ESV Study Bible (Kindle Locations 277848-277859). Good News Publishers/Crossway Books. Kindle Edition.