The instrument of obedience removed.
The instrument of obedience was a star-shaped device that was implanted subdermally in the right temple of each inhabitant of the Fabrini asteroid-ship Yonada.
At some point during a Fabrini's life, the instrument was inserted by a hand-held mechanism operated by the high official. This event marked the individual's becoming one of the People of Yonada. Presumably all those born on Yonada underwent the ritual. Outsiders could as well, since Dr. Leonard McCoy underwent this initiation in 2268 following his brief resignation from Starfleet.
Natira prepares to implant the instrument of obedience
The instrument apparently monitored an individual in an undetermined manner to detect offensive behavior, including (but not limited to) questioning the Oracle, engaging in any of various acts defined as sacrilege, or speaking (and presumably believing) things that contradict the official doctrine of the faith.
Offenders experienced pain inflicted through the instrument; repeated offenses caused increasing pain and eventually death. When operating, the device glowed red brightly enough to be seen through the skin. The Oracle monitored and probably operated the instrument, as it was aware of offenses requiring punishment.
McCoy is stricken by the instrument of obedience
The USS Enterprise landing party learned that the Yonada was constructed to save a remnant of their people from an impending supernova. The Oracle was presumably installed at that time and given suzerainty over these people.
During the ritual that implanted an instrument and made him one of the people, McCoy learned the location of the Book of the People. Correctly surmising that it contained the information necessary to locate the control center, a prerequisite for returning Yonada to its proper course, McCoy called his former commander and told him where to look for the book. For this act of sacrilege, the Oracle used McCoy's instrument to inflict horrible pain, rendering the doctor unconscious. Only Spock's timely intervention in removing the instrument saved McCoy from permanent harm or death. (TOS: "For the World is Hollow and I Have Touched the Sky")
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Apocrypha[]
The novel Ex Machina posited that the devices were initially created to keep convicted criminals from behaving in an undesirable manner, and were only implanted in such individuals. The novel further posited that the winners of an internecine struggle a few thousand years after Yonada's launch reprogrammed the Oracle and gave it authority over the people of Yonada. Ex Machina explained that this group of Yonadans felt the need to take drastic actions to ensure the colony's survival, and they created a framework that suppressed violence and replaced individual initiative with dogma. The plan succeeded, since the Yonadans survived to disembark, but their theocratic past created conflicts between those who wished to retain the Oracle and those who felt it had served its purpose and wished to discard it.