The autonomic nervous system was an extension of a biological organism's central nervous system. The autonomic nervous system controlled the respiratory system and other internal organs in the thorax of a lifeform.
According to Doctor Roger Korby, one of the steps in making an android duplicate was to synchronize synthetic organs with the autonomic nervous system of a biological lifeform, duplicating the rhythms of the body. Korby used the process to make an android duplicate of Captain James T. Kirk in 2266. (TOS: "What Are Little Girls Made Of?")
When Spock's brain was surgically removed by Kara in 2268, his autonomic functions continued until life support took over. Doctor McCoy claimed it was a testament to Vulcan physiology. (TOS: "Spock's Brain")
One of the dead Memory Alpha technicians found by the crew of the USS Enterprise in 2269 died from severe brain hemorrhaging due to distortion of all neural systems and the dissolution of her autonomic nervous system. (TOS: "The Lights of Zetar")
A genetically-engineered microvirus was discovered to have killed Volnoth in 2366. The virus killed by blocking autonomic nerve impulses in beings with a specific DNA sequence. (TNG: "The Vengeance Factor") Another engineered virus, the aphasia virus created by Bajoran scientist Dekon Elig, attacked the autonomic nervous system of those it infected. In 2369, the virus was inadvertently activated on board Deep Space 9, infecting many of the crew. (DS9: "Babel")
The stasis systems of Viorsa's species required a secure link to the autonomic nervous system to induce artificial hibernation. The crew of the USS Voyager encountered the stasis system in 2372. (VOY: "The Thaw")
During a medical procedure in 2373, Tom Paris went into respiratory arrest. The Doctor and Kes applied an ethorin pulse to stabilize his motor neurons, and his autonomic and somatic systems returned to normal. (VOY: "The Swarm") Later that same year, the Voyager encountered the Voth, which used hibernation as a form of protection when captured. The Doctor noted that the species' autonomic nervous system remained fully functional during hibernation. (VOY: "Distant Origin")
In 2376, a Borg maturation chamber housing an infant drone malfunctioned aboard a Borg cube, causing the drone's autonomic nervous system to begin failing. Seven of Nine had the infant drone transported to the USS Voyager in an effort to save it. (VOY: "Collective")