A clear and succinct summary of this word (never try to say it with food in your mouth and people standing close by). Propitiation fell out of favor with many 20th century theologians and the Church’s theology of atonement has suffered mightily for it. See what you think.
Here’s what I mean: Propitiation is an ancient word, which we as Christians have in common with other world religions. To propitiate a god is to offer a sacrifice that turns aside the god’s wrath. Anyone who believes in a god knows that they need some way to stay on the friendly side of that god. So they give gifts to the god, or serve in the temple, or give alms. And if the god is angry with them, they pay a price, or make a sacrifice, or find some way to soothe the god’s anger: they propitiate him.
In pagan propitiation, the gods need to be propitiated because they are grumpy and capricious. They don’t care much about humans except when something makes them angry; then they smite! And it’s up to humans to get busy doing the propitiating, to make up for whatever they’ve done that angered the gods. The humans find something that the gods like (sweets, or meat, or pain, or blood), and offer it as a bribe to calm down their wrathful deities.
But every aspect of biblical propitiation contrasts with the pagan kind.