There are two common causes of infection: cavities and fractured/broken teeth. Both expose the pulp area to bacteria that live in saliva. These bacteria can cause an infection that can kill the pulp.
Without treatment, pus from the infected tooth can spread to the root tip and eventually pass ot the jaw bone. This can cause an abcess (a pus pocket) that can damage the bone that surrounds the tooth. The pressure this causes can cause excruciating pain and, left untreated, can be life threatening. An infected tooth can not heal on its own and will only get worse.
Symptoms tend to vary from patient to patient. Infected teeth may be sensitive to hot or cold, the area may be swollen or painful, or there may be a bad taste in the mouth. Occasionally there will be no symptoms at all.