Spectres are agents from the Office of Special Tactics and Reconnaissance and answer only to the Citadel Council. They are elite military operatives, granted the authority to deal with threats to peace and stability in whatever way they deem necessary.
They operate independently or in groups of two or three. Some are empathetic peacekeepers, resolving disputes through diplomacy. Others are cold-blooded assassins, ruthlessly dispatching problem individuals. All get the job done, one way or another, often operating outside of the bounds of galactic law.
The Spectres were founded after the salarians joined the Council. For many years, they operated in secrecy, as back-room "problem solvers". Only after the Krogan Rebellions did their activities become publicized. Assignment of a Spectre is less contentious than military deployment, but makes it clear that the Council is concerned about a situation.