The ANS is also known as the Visceral Nervous System and its job it to maintain homeostasis (balance) in the body between arousal and relaxation in various systems. It mostly controls unconscious, involuntary actions such as breathing, pupil dilation, and perspiration. You can think of the ANS as a regulation station in your body. It keeps blood vessels and blood pressure at a normal level, works with the hearts electrical impulses (and thus helps it contract), and many other things.
Here is a website that introduces issues that can arise from an unhealthy ANS: http://www.americanheart.org/presenter.jhtml?identifier=4463