Adrian Ow has a good post explaining the definition of propitiation:
Simply spelt out, it speaks of mending the relationship with that someone who's angry by something you did. This brings out a new dimension that someone, somewhere is angry. And in the context of the Bible, 'propitiation' paints a clear picture that God is angry with us. Why? Sin. Sin absolutely repulses God. Sin absolutely disgraces God's holy name. In fact, from Rom 3:23 (look above), sin is to “fall short of God's glory”. Therefore, angry is too... mild a word to begin describing God's attitude toward sin. Rather, the word 'Wrath' is used to describe this strong, holy, divine anger that God has toward sin. Therefore, ‘Propitiation’ brings forth the point that God’s wrath is against all man because of how they have desecrated his glory. And God's holiness, justice and righteousness disallows sin to be let off scot-free.... In a nutshell, this is propitiation: God averting his wrath toward man through the death of His Son.
Adrian also looks at how various translations translate 1 John 2:2. (“He is the propitiation for our sins, and not for ours only but also for the sins of the whole world.”) Adrian thinks that the ESV and others get it right when they use the English word propitiation here.
The ESV Preface says that the ESV “retains theological terminology--words such as… propitiation--because of their central importance for Christian doctrine and also because the underlying Greek words were already becoming key words and technical terms in New Testament times.”
For another view, see the NET Bible’s footnote to 1 John 2:2.