Anesthesiologists are responsible for a variety of tasks and work in many different medical facilities. The role they are most well known for, and a primary part of their job, is administering anesthetics to patients so that they are not in pain during an operation. In this situation they are responsible for more than just administering the anesthetic.
They meet with the patient to check the patients overall health and to see if they are healthy enough to handle an anesthetic. Once they have done this, just before the surgery, the anesthesiologist administers an anesthetic. They administer either a general or local anesthetic to the patient. Once the patient is in surgery, the anesthesiologist watches over the patient to ensure that their vitals remain at the right levels. If they feel that the patient's vitals are at dangerous levels at any point in the operation, they can actually tell the surgeon to stop the operation.
They also help with pain management during childbirth. They discuss pain management options with the mother, and administer an epidural anesthetic if the mother decides that she wants it. They watch over the mother and if the labor is long, or the epidural wears off, they provide another dose.
They also work with patients who need pain management for other issues outside of the operating room and delivery room. They provide after care for patients who have had surgery and still require some sort of pain management. They may also work in emergency rooms, and help with patients who need immediate pain relief or sedation.