King James Bible Dictionary

That by which God is rendered propitious, i.e., by which it becomes consistent with his character and government to pardon and bless the sinner. The propitiation does not procure his love or make him loving; it only renders it consistent for him to execise his love towards sinners.

In Romans 3:25 and Hebrews 9:5 (A.V., "mercy-seat") the Greek word hilasterion is used. It is the word employed by the LXX. translators in Exodus 25:17 and elsewhere as the equivalent for the Hebrew kapporeth, which means "covering," and is used of the lid of the ark of the covenant (Exodus 25:21; 30:6). This Greek word (hilasterion) came to denote not only the mercy-seat or lid of the ark, but also propitation or reconciliation by blood. On the great day of atonement the high priest carried the blood of the sacrifice he offered for all the people within the veil and sprinkled with it the "mercy-seat," and so made propitiation.

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 our guilt, covered it, by the vicarious punishment which he endured. (Comp. Hebrews 2:17, where the expression "make reconciliation" of the A.V. is more correctly in the R.V. "make propitiation.")

General references
Romans 3:25; Romans 5:1; Romans 5:10-11; 2 Corinthians 5:18-19; Colossians 1:20-22; 1 John 2:2; 1 John 4:10; Hebrews 9:5
Atonement

PROPITIATION, noun propisia'shon.

1. The act of appeasing wrath and conciliating the favor of an offended person; the act of making propitious.

2. In theology, the atonement or atoning sacrifice offered to God to assuage his wrath and render him propitious to sinners. Christ is the propitiation for the sins of men. Romans 3:25. 1 John 2:2.