Council Security is a civilian agency within the Fleet responsible for security considerations of the civilians. They guard the Quorum of Twelve and have jurisdiction over the prisoners of the Prison Barge (Baltar's Escape).
Much like Colonial Warriors, they are armed with laser pistols and apparently have a presence aboard Galactica.
View on Council Security by the Warriors
It is evident that Council Security was viewed with disdain by Colonial Warriors (Greetings from Earth, Baltar's Escape). For instance, Colonel Tigh comments to Siress Tinia that Council Security couldn't stop an escape from the Orphan Ship (Baltar's Escape).
In addition, due to the color of their uniforms, they are also referred to as "blackshirts".