Pacifier is a social skill. It appears to be useful for calming down tantruming dwarves. It has been observed that an angry dwarf has stopped and calmed down after talking with someone with Novice Consoler or Novice Pacifier. This is indicated within its thoughts/mood screen.
Pacifier produces the thoughts: "...yelled at somebody in charge and felt <a little / a lot> better afterward." and "... was yelled at by an unhappy citizen recently."
Skilled pacifiers probably calm dwarves down more easily. Sometimes an attempt to pacify someone will fail. The chance of this is likely also decreased by skill in pacification.