Pelagianism is a belief that original sin did not taint human nature (which, being created from God, was divine), and that mortal will is still capable of choosing good or evil with no Divine aid whatesoever. Thus, Adam's sin was "to set a bad example" for his progeny, but his actions did not have the other consequences imputed to Original Sin. Pelagianism views the role of Jesus as "setting a good example" for the rest of us (thus counteracting Adam's bad example). In short, humanity has full control, and thus full responsibility, for its own salvation in addition to full responsibility for every sin (the latter insisted upon by both proponents and opponents of Pelagianism).
It is debatable whether the monk and moralist Pelagius actually advocated such an extreme view. Some argue that Pelagius may be more correctly labelled a "Semi-Pelagian", due to the opinion that his views were exaggerated by Augustine of Hippo and Jerome, which views later came to be known as "Pelagianism." Pelagianism was opposed by Augustine, leading to its condemnation as a heresy at several local synods. These condemnations were summarily ratified at the Council of Ephesus, although it was not considered a major act of that council.
See also: Semipelagianism, Charles Finney