whom God hath set forth -- (προέθετο proetheto). The word properly means, “to place in public view;” to exhibit in a conspicuous situation, as goods are exhibited or exposed for sale, or as premiums or rewards of victory were exhibited to public view in the games of the Greeks.
It means that God has publicly exhibited Jesus Christ as a propitiatory sacrifice for the sins of people. This public exhibition was made by his being offered on the cross, in the face of angels and of people. It was not concealed; it was done openly.
a propitiation -- (hilastērion). The only other N.T. example of this word is in Hebrews 9:5 where we have the “cherubim overshadowing [concealing, covering, hiding] the mercy seat” (to hilastērion). It refers to the act of getting rid of sin which has come between God and man.
Septuagint usage. These words mostly represent the Hebrew verb kaphar to cover or conceal, and its derivatives.
*** Paul presents a very graphic picture to the Jewish mind of the blood of atonement being sprinkled upon the mercy seat for reconciliation by the high priest. In this picture Paul presents Jesus’ blood as the sacrifice that covers our sins before God.
sacrifice of atonement.… The word translated “sacrifice of atonement” is ἱλαστήριον (hilastērion), which is also used in Hebrews 9:5. This term and its equivalent, ἱλασμός (hilasmos) (1 John 2:2; 1 John 4:10) stand for one of the most important concepts in the Bible.
..it is used often in the LXX and in Hebrews 9:5 to refer to the lid of the ark of the covenant, i.e., the “mercy-seat,” many find that meaning figuratively here in Romans 3:25. Just as the mercy-seat was the place where the atoning blood of sin-offerings was sprinkled in OT times, so also is Jesus in a sense the place where the final atonement has been made for all times. - CPNIV
Paul more likely intends it to mean the atoning sacrifice itself, in the sense of a propitiation.
The key element in the concept of propitiation is the averting of wrath. To say that Jesus is a propitiation means that he offered himself as a sacrifice that turns God’s wrath away from deserving sinners by accepting that wrath upon himself in our place. Thus he is a “wrath-removing sacrifice” (Hendriksen, I:132), a “wrath-averting sacrifice” (Moo, I:237). - CPNIV
through faith, by [in] his blood -- (dia pisteōs en tōi autou haimati). So probably, connecting en toi haimati (in his blood) with proetheto. - RWP
We are justified (made right with God) by our faith in the blood of Christ as the atoning price giving (sacrificed) for our sins.
through faith -- "Our faith", God’s grace is shed on us for "our faith" in Jesus’ blood as atoning sacrifice made for sin.
[He did this] to demonstrate [declare] his justice -- εἰς ἔνδειξις eis endeixis. For “the purpose” of showing, or exhibiting; to present it to man.
The meaning is that God’s scheme of redemption was publicly manifested to the people demonstrating his plan for justification.
his justice [righteousness] . .Some interpreters understand this as referring to an attribute of God (see Romans 1:17), but the whole context may be indicating this is not speaking of an attribute of God, but of his "plan" for justifying sinners. He has adopted a plan by which people may become justified by faith in Jesus Christ, and not by deeds of law, which they couldn’t keep in the first place. - BN
justice [righteousness] -- it means God’s own righteous character, his inner integrity that requires him to be completely true to himself in all ways. - CPNIV
in His forbearance -- Through his patience, his long-suffering. That is, he did not come forth in judgment when the sin was committed; he spared us, though deserving of punishment; and now he comes forth completely to pardon those sins concerning which he has so long and so graciously exercised forbearance. - BN
God not remitting but only forbearing to punish them, or passing them by, until an adequate atonement for them should be made. -JFB
God had passed over the sins -- “Passing over.” The word used here πάρεσιν paresin occurs no where else in the New Testament, nor in the Septuagint. It means “passing by,” as not noticing, and hence, forgiving. A similar idea occurs in 2 Samuel 24:10, and Micah 7:18. - BN
previously committed [committted beforehand; former sins] -- That have been committed; or that have existed before. This has been commonly understood to refer to past generations, as affirming that sins under all dispensations of the world are to be forgiven in this manner, through the sacrifice of Christ. [But Barns doesn’t believe that to be the meaning] - BN
Human sin, past, present, and future, is dealt with by Christ’s sacrifice. ... This was a past act of God’s grace looking forward to Christ’s work (cf. Acts 17:30; Romans 4:15; Romans 5:13) - Utley