The propitiation place is typified in Exo. 25:17 by the sin-covering lid on the ark. The ark was the place where God met with people. In the ark was the law of the Ten Commandments, which by its holy and righteous requirement exposed and condemned the sins of the people who came to contact God. However, by the lid of the ark, with the propitiating blood sprinkled on it on the Day of Propitiation, the entire situation on the sinner's side was fully covered. Therefore, upon this sin-covering lid God could meet with the people who broke His righteous law, and He could do this without, governmentally, any contradiction to His righteousness, even under the observing of the cherubim that bore His glory and overshadowed the lid of the ark. Thus, the problem between man and God was appeased, enabling God to forgive and be merciful to man and thereby to give His grace to man. This is a prefigure of Christ as the Lamb of God taking away the sin that caused man to have a problem with God (John 1:29), thus satisfying all the requirements of God's holiness, righteousness, and glory and appeasing the relationship between man and God. Hence, God could pass over the people's sins that had previously occurred. And, in order to show forth His righteousness, He had to do this. This is what this verse refers to.
The Hebrew word for the lid of the ark is kapporeth, from a root meaning to cover. In the Septuagint this word is translated hilasterion, which means the place of propitiation (implying to forgive and to give mercy — the word rendered propitious in Heb. 8:12 is the root of hilasterion, and the word rendered propitiated in Luke 18:13 is derived from this root). The King James Version adopts the rendering "mercy seat," referring to the place where God grants mercy to man. In Heb. 9:5 Paul also used hilasterion for the lid of the ark. Here, in Rom. 3:25, the same word, hilasterion, is used to show that the lid of the ark signifies Christ as the propitiation place set forth by God.
In addition to hilasterion, two other words derived from the same Greek word as hilasterion are used in the New Testament to show how Christ took away man's sin to appease the relationship between man and God. One is hilaskomai (Heb. 2:17), which means to propitiate, that is, to appease, to reconcile one by satisfying the other's demand; the other is hilasmos (1 John 2:2; 4:10), which means that which propitiates, that is, a propitiatory sacrifice. Christ made propitiation for our sins (Heb. 2:17); hence, He has become that which propitiates, the propitiatory sacrifice, between us and God (1 John 2:2; 4:10), and He has also become the place, as typified by the lid of the ark (Heb. 9:5), where we enjoy propitiation before God and where God gives grace to us.