Everything Talei said is correct but my textbook also briefly covers the enteric nervous system which is a sub-division of the autonomic nervous system, responsible for the gastro-intestinal/digestive tract.
I'm not sure if you'd lose marks for not including it (my geuss would be probably not but don't quote me on that) but it wouldn't hurt to include.
To answer the question as a whole it's important to identify each branch and it's subdivisions before giving a breif but accurate explaination of what they do, so my answer to the question would be this:
The nervous system has two primary parts, the central nervous system and the peripheral nervous system.
The central nervous system is comprised of the brain and the spinal chord and is responsible for processing the information from stimulus both inside and outside the body and coordinating the body's responses and activities.
The peripheral nervous system are a network of nerves that convey messages to and from the central nervous system via the spinal chord with two main branches, the somatic nervous system and autonomic nervous system.
The somatic nervous system is responsible for communicating sensory information to the brain and sending the responding motor information to skeletal muscles to control voluntary movements.
The autonomic nervous system is responsible for sub-conscious responses and behaviour with 3 branches, the sympathetic nervous system, the parasympathetic nervous system and the enteric nervous system.
The sympathetic nervous system is responsible for controlling the body's flight or fight response after percieiving a fer trigger or experiencing a crisis, such as by increasing the body's breathing rate and producing hormones like adrenaline and cortisol.
The parasympathetic nervous system is responsible for maintaining homeostasis or balance within the body, and is typically the dominant system over the sympathetic nervous system. The parasympathetic nervous system helps gradually reduce the effects of the sympathetic nervous system to return the body to a calm state once the individual is out of danger.
The enteric nervous system is responsible for controlling the body's digestive or gastrointestinal tract such as controlling nutrient absorption and hormone release within the gut.
I am a current year 12 psych student this year so I can't say with certainty what I'm doing is correct so if anyone corrects me I'll take any feedback on board and my information may not be the best as I'm still learning the topic as well.
I hope this could be of some help and I'm sorry if it isn't.