First, Some History
Jacobus Arminius (1560-1609) was a Dutch theologian during the later period of the Protestant Reformation. Arminius and his followers opposed some points of Reformed theology, which developed more robustly out of the writings and teachings of some of the Reformers. Reformed theology is a label thrown around by many Christians today, but fundamentally it refers to the theological affirmations contained in the Three Forms of Unity - the Belgic Confession, the Heidelberg Catechism, and the Canons of Dort. One of the most (maybe the most?) influential systematic treatments of Reformed theology is John Calvin's Institutes of the Christian Religion.
Though Calvin and Arminius never met (Calvin died when Arminius was 4 years old), Arminius admired Calvin and his outstanding biblical hermeneutics. Arminius once said, “Next to the study of the Scriptures… I exhort my students to read Calvin’s Commentaries carefully and thoroughly… for I affirm that he excels beyond comparison in the interpretation of Scripture.”
Arminius and his followers (originally called the Remonstrance at the Synod of Dort) did, however, disagree with some points of the Reformed teaching in the area of soteriology (i.e., the doctrine of salvation). Forty-two ministers organized their opposition to some Reformed teaching, focusing in on five particular disputed points.
These points became the five-point dividing line between what later came to be called Arminianism and Calvinism.
Ironically, the five-point dividing line became known as "The Five Points of Calvinism," though Calvin himself had never arranged them as such. The five points or doctrines were not even a bulleted theological structure until after the Remonstrance made them the focus of their opposition (50 years after Calvin died!). And at that time the five affirmative doctrinal points were not arranged with the acronym TULIP. That didn't happen until at least 200 years later.
Defining Arminianism
The Five Articles of the Remonstrance represent historic Arminianism. An Arminian, in the technical sense, is someone who affirms the Arminian articles or points over against the Calvinistic or Reformed points.
The Five Articles of the Remonstrance:
1) Conditional Predestination: God predestines some sinners for salvation, and this predestination is conditionally based on God’s foreknowledge about each person’s anticipated faith or unbelief.
2) Universal Atonement: Christ died for all humans, and God intended His sacrifice for all humans, but only those sinners who accept this atoning work will be saved.
3) Saving Faith: Sinful and Fallen humanity is unable to attain saving faith unless he is regenerated and renewed by God in Christ through the Holy Spirit.
4) Resistible Grace: The grace of God is effective but resistible, so man must cooperate with God’s grace to bring about personal salvation.
5) Uncertainty of Perseverance: Although God’s grace is abundant, the sinner can lose that grace and become lost even after he has been saved.
Common Conversations Today
It is important to note that some Arminians may not affirm all five of these articles or affirm each of them with the same fervor. In recent history, the Arminian system (or some variation of it) has been the most commonly held view among American Evangelicalism (measuring by sheer numbers). Though, most Evangelicals do not seem to be aware of the historical grounding of their doctrinal views.
The Arminian view is widely embraced among many Southern Baptists, and it is the official doctrinal position of Methodists, Nazarenes, and Wesleyans. C.S. Lewis, A.W. Tower, and Adrian Rogers are three notable men who affirmed (at least generally) an Arminian position. There are others, but these are significant voices, and each represents a distinct platform among culture and Christianity (even today).
This brief article is only intended as a very simple introduction to this theological system. I suggest further investigation for the interested Christian, and numerous books and articles might be a help.
In my estimation, Wayne Grudem's book, Systematic Theology, does a good job of explaining the various views of biblical salvation. This would be a good starting point for further study.
Whether you embrace this view or not, it is vital that all believers look to the Bible as the ultimate authority. It is also important that we humbly and graciously investigate the Bible alongside our brothers and sisters in Christ. While we may disagree, it would do us well to show love and charity to those who are on the other side of the fence from us.