"Having dealt with the linguistic level, let’s kick it up to the theological level. What does propitiation mean theologically? Those who would argue that the idea taken literally is more suited to pagan than to Christian theology are correct. Pagan deities might literally feel passions like anger, but Christian theological had established long before the time of Trent that God does not literally have passions (see Aquinas on this point). As a result, when God is described as being angry or hating something, such as sin, there is a figurative component to the language (again, see Aquinas on this point).
When people sin, God is not literally burning with anger, because his infinite beatitude cannot be diminished by what creatures do. Instead, as Aquinas and Catholic theology in general points out (see Ott’s discussion of this), Scripture and the Magisterium are using language with a figurative component when they speak in this way.
The same component is present when the language of propitiation is used with regard to God. To say that God has been propitiated does not mean that he has stopped burning with anger (something he was not doing in the first place) but that the person now will not experience the painful consequences of sin that he otherwise would have experienced. The sacrifice of the Mass, by bringing about this state of affairs by applying the fruits of Christ’s sacrifice, is thus propitiatory."
From:
jimmyakin.com/2004/03/and_speaking_of-4.html