"Propitiation" must be a very rare word, because the only time I have ever heard it used is when speaking of its use in the Bible. It appears in the King James Version only three times: Romans 3:25; 1 John 2:2 & 4:10. It is translated "mercy seat" once in Hebrews 9:5. Webster's Dictionary defines it as an act which causes one to become favorable or to regain a position of good will. The reference in Hebrews describes the place where propitiation takes place. The mercy seat was the top surface of the Ark of the Covenant. It was there that the high priest sprinkled the blood of the sacrifice once a year for the sin of Israel. Hebrews 9:11-28 teaches that the Old Testament sacrifice was a picture of what would take place when Christ, as our High Priest, would offer His own blood, once for all of humanity (John 3:16).
One might ask why was Christ's death necessary to forgive my sins? In actuality, it was only necessary that He die for those of us who are sinners. And, since all have sinned (Romans 3:23), and the wages of sin is death (Romans 6:23), someone had to die for my sin, if I was to spend eternity with my Creator. Hebrews 9:22 says that without the shedding of blood, there is no remission (forgiveness of sin). In a sense, the word "blood" and the word "life" are interchangeable, so when the Bible speaks of Jesus shedding His blood for us, it means that He gave His life (Leviticus 17:11). Propitiation satisfied God's Law and, in a sense, it is the reason we will be resurrected from the dead. Our High Priest entered the Holy of Holies in heaven and, by placing His own blood on the Judgment Seat, transformed it into the Mercy Seat.
The awesome thing about this act of love for humanity, is that in God's plan for us, it was counted as being a done deal before He began creation. Jesus was called "the Lamb of God Who taketh away the sin of the world" by John the Baptist (John 1:29). Not only was Christ's sacrifice counted before this world was formed, those of us who accept Jesus as Lord and Savior had our names written in "the Lamb's book of life," which was also written before creation (Revelation 13:8). God knew we would sin, and He paid for us with the blood of His Son. Jesus paid for the sin of the whole world, but only applies to those who receive Him (John 1:12).
Propitiation, while only translated as such three times, has a great deal of significance to the believer. It means that we will appear before Him as sinless, and thereby satisfy God's requirement that we be as holy as He. Did we earn it? No! God's Gift to the world was Jesus Christ. He is both Grace and Mercy to us.