This debate has come up around me several times this week, and I thought I'd share a few notes on the topic. [This document was edited on December 27th, 2012 - WRF]
All definitions below are from either The American Heritage College Dictionary, 3rd edition, or Liddell & Scott's Greek-English Lexicon, or The New College Latin & English Dictionary, depending on the language of the word being defined. They are abridged, and some of my own comments are added.
Propitiate: to conciliate, appease.
Propitiation: The act of propitiating. Latin propitius, a disposition of favor (one can think pro-pity, a setting forth of pity or mercy). The Greek word translated propitiation in the New Testament is hilasmos, which is a means of appeasing, a conciliation.
To appease: to bring peace or calm, to satisfy or relieve.
To atone: to make amends or reparations for an injury or wrongdoing, to expiate.
The only time we see the word "atonement" in the popular versions of the New Testament is at Romans 5:11, but the Greek word is katallage, and it means reconciliation. Modern versions such as the NAS and ASV have recognized this and translate the word as reconciliation. It does not ever mean atonement, and it cannot mean atonement. Therefore, the word atonement does not appear in the New Testament, unless one is an advocate of "Church Greek", which is not the Greek of our Redeemer and His apostles who spoke and wrote Koine Greek.
Therefore the word atonement is not found in the New Testament. Christians confuse propitiation and atonement, however these are not the same, although the "Church Greek" devisors would like Christians to confuse them. The devisors of "Church Greek" want to confuse these terms, because they strive to eliminate the idea of Christ's propitiation as an act of conciliation between Israel and Yahweh our God, endeavouring to destroy the racial covenants between Israel and Yahweh. The matter of reconciliation stands in the way of the universalism of the "Church".
Christ is not our Atonement, He is our Propitiation, and there is a world of difference. We can never fully make our atonement, because we cannot ever repay Yahweh for our sins, national or personal. Therefore we need His propitiation. As Paul explained in the same chapter of his epistle to the Romans, earlier in the same paragraph, “But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.” The idea of atonement requires an action on the part of one making an atonement, where the idea of propitiation requires no such action.
Under the New Covenant our reconciliation with Yahweh is consciously effected upon our acceptance of the propitiation of Christ, but atonement was not on the cross. He effected our propitiation on the cross whether we are conscious of it or not. He can make a propitiation for us, but He cannot make amends for us, paying Himself back for our sins on our behalf. Our conciliation is achieved by our acceptance of His propitiation, if indeed He accepts us, and that is the only manner by which we can make atonement. Eventually all Israel will accept His propitiation!
We all have some judaeo baggage to lose if we are ever going to come to a better knowledge of the truth.
William Finck, Christogenea.org