The security service tasked with protecting President of the Colonies, Laura Roslin. They were hand picked by Capt. Lee Adama from civillians in the Fleet. Responsible to Roslin, and answerable only to Roslin, they have no allegiance to the Galactica personel. They are former police, security personel, or people with some kind of firearms training.
The security detail protecting Colonial One is a distinct entity from the Marines and the Colonial Fleet personel aboard Galactica. Apollo himself had intentionally designed their organization this way, because he thought they should have a separate command structure from the military organizations, so the lines of authority establishing who was under whose control would not be confused.
When Commander Adama sent Marines led by Col. Tigh and Apollo to Colonial One to arrest President Roslin, they engaged in a tense standoff with her security detail. Eventually, Apollo pulled a gun on Tigh, then Roslin told him to stop and that she would go peacefully ("Kobol's Last Gleaming, Part II").
Note
This is not it's official name, but they aren't really a "Secret" Service. Ron D. Moore discusses them in his podcast for Kobol's Last Gleaming, Part II.