A tooth's nerve is not vitally important to a tooth's health and function after the tooth has emerged through the gums. Its only function is sensory - to provide the sensation of hot or cold. The presence or absence of a nerve will not affect the day-to-day functioning of the tooth.
When a tooth is cracked or has a deep cavity, bacteria can enter the pulp tissue and germs can cause an infection inside the tooth. If left untreated, an abscess may form. If the infected tissue is not removed, pain and swelling can occur. This can not only injure your jawbones, but it is detrimental to your overall health. Without the proper treatment, your tooth may have to be removed.