Consoler is a social skill. It appears to be useful for comforting dwarves after they lose something (a family member, a masterpiece, etc.) and would otherwise begin tantruming. It has been observed that a tantrumming dwarf has stopped and calmed down after talking with someone with Novice Consoler or Novice Pacifier. This is indicated within both dwarves' thoughts/mood screen.
Consoler produces the thoughts: "... cried on somebody in charge and felt <a little / a lot> better afterward." and "... was cried upon by an unhappy citizen recently.".
Skilled consolers probably calm dwarves down more easily. Sometimes an attempt to console someone will fail. The chance of this is likely also decreased by skill in consoling.