Pelagianism is a heretical Christian doctrine developed by a British monk named Pelagius around 400 AD. Although he was British, Pelagius mostly wrote in Rome, where he came to the attention of the Roman Catholic authorities who have declared his teachings heretical on numerous occasions, the first being at the Council of Carthage in 412.
Pelagianism denied the Catholic doctrines of original sin, the divinity of Jesus, and salvation by grace. Pelagius held that salvation was achieved through one's own efforts, and was not a gift from God. Pelagianism also taught that human beings were born in a state of innocence with a nature that was as pure as that which Adam was given at his creation, hence there is no need to baptize infants and small children, nor any need for them to confess (before the age of five) that they have sinned and come short of the glory of God.
As a result of his basic assumption, Pelagius taught that man has an unimpaired moral ability to choose that which is spiritually good and possesses the free will, ability, and capacity to do that which is spiritually good. This resulted in a gospel of salvation based on human works, in opposition to the Catholic doctrine of salvation by being baptized into Christ. Pelagianism is evident in any doctrine that teaches that man can choose to follow the precepts of God because he has the power within himself to do so, without having any need for the assistance of God's freely bestowed, universally available gifts of grace.
It should be noted that some Calvinist theologians, when debating those who oppose Calvinism, will automatically label their opponent as supporting Pelagianism (or Semi-Pelagianism) even if the opponent is not.