What does it mean that Jesus is our "Propitiation" or "Sacrifice of Atonement"?

Beale's Reason as Reason the CSB made a good choice

For more on "mercy seat" as propitiation see G. K. Beale, A New Testament Biblical Theology: The Unfolding of the Old Testament in the New (Grand Rapids, MI: Baker Academic, 2011), 486–490.

The word hilastērion has been highly debated during the past century. Some want to see it involving a notion of “propitiation”: the forgiveness of the penalty of sin by means of a substitute who assumes the penalty (e.g., KJV, NASB, ESV, HCSB). Others prefer the idea of “expiation”: the forgiveness or sending away of sin by Christ’s death but without a penal substitutionary notion, though also without any explanation of how sin is sent away (e.g., RSV). The NET has “mercy seat.” Some translations are ambiguous and have translations such as “sacrifice of atonement” (NRSV, NIV) or “sacrifice for reconciliation” (e.g., NJB). I believe that the best translation is “mercy seat” (not an adjective but rather a neuter singular accusative noun), which refers to the golden lid of the ark of the covenant. This is its meaning in the only other use of hilastērion in the NT (Heb. 9:5). The same Greek word occurs twenty-eight times in the LXX and almost always refers to the lid of the ark of the covenant—that is, the mercy seat (also always there a neuter singular noun).

It is likely that Paul is referring to the mercy seat in the holy of holies, since he has introduced this paragraph by saying that the declaration of righteousness that he is about to speak has been “witnessed by the Law and Prophets” (Rom. 3:21) (486-7).

Beale gives the meaning of "mercy seat" applied to Jesus in Romans 3.25 when he writes:

Paul is drawing on that aspect of atonement at the mercy seat dealing with ransom by means of the blood of a penal substitute (hence the suitability of mentioning Christ’s blood only a few words later in Rom. 3:25). Christ is now the place where God’s penal wrath is poured out for sinful humans, who deserve the condemnation. What was done in the old temple in the secrecy of the holy of holies is now “displayed publicly.” Part of the core of the temple, the mercy seat of the ark, is identified with Jesus, likely portrayed as the beginning of the eschatological temple, to which the old temple ark pointed (so that, perhaps, there is a nuance of Christ as the atonement, which consecrates the new temple) (489).