Occasionally mentioned around the edges of other story elements, I think as Operatives of the Presidium?
I don’t suppose I’ve missed a blog entry somewhere giving more details on who these are, and how they fit into the Conclave’s big picture, and who gives them marching orders? From memory, the Conclave as a whole doesn’t have a military any more than it has a taxation office, so I’m curious as to what lead it to have Spectres.
It’s not like the Citadel Council has a military, either. (The Citadel Fleet is mostly seconded to C-Sec by the turians, Destiny Ascension notwithstanding, just as the Conclave Drift is guarded by the seconded Fifth Flotilla.)
As for why they exist, that would be the same reason that the Spectres exist. On occasion, the Presidium (to whom they answer) perceives threats to galactic stability. The Operatives are there to solve the problem.
(And provide the valuable service/diplomatic fig-leaf of solving the problem in a way that is not tied to any particular polity’s trouble-shooting services. On those occasions when it is convenient for the message to be “The civilized galaxy disapproves,” rather than “You have angered the gazebo/Imperium/League/Network/Echelons/Other League.”)