The "Right to Life" is a belief that all humans have a natural right to live and to continue living. Those who oppose abortion believe that a human fetus is a human being and also has the right to life. Right-to-life organizations can claim some fairly major recent victories, including a favorable Supreme Court opinion that ended the practice of partial-birth abortion.
Some people who consider themselves "right-to-lifers" make exceptions to allow abortion if the pregnancy resulted from rape or incest, or if the mother's life was in danger if the pregnancy carried to term. Others would make no exceptions for any reason since a human life is a human life regardless how it was created.