The nerve of a tooth is not vital to a tooth's health and function after you have your permanent adult teeth. Its only function is to sense hot or cold. Whether the nerve is there or not 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 result. 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.