Final answer:
The division of the autonomic nervous system that operates at an unconscious level is the parasympathetic nervous system, responsible for 'rest and digest' functions.
Step-by-step explanation:
The division of the autonomic nervous system operating at an unconscious level is known as the parasympathetic nervous system. This division is responsible for the 'rest and digest' activities, counterbalancing the sympathetic nervous system, which prepares the body for 'fight or flight' situations. Both divisions work together to maintain the body's homeostasis, with the parasympathetic nervous system becoming predominant when the body is at rest or in a non-stressful state, slowing down the heart rate, and promoting digestion and restoration.