Answer:

Jacobus Arminius (1560–1609) was a member of the Dutch Reformed Church. He studied John Calvin's beliefs at the Genevan Academy but concluded that Calvin was wrong on some of his points.

Arminius accepted that people were born sinful (see Total Depravity or Total Inability as to why his belief was wrong). Because of this sinfulness, Arminius believed that they could not save themselves without aid from God. Thus, God gives grace to those men God believes could have sufficient faith so as to be saved. This grace allows men to choose whether to follow God or not. John Wesley further refined this idea and it was called prevenient grace. See What is prevenient grace? for an analysis of why the belief is wrong.

Since free will is involved, Arminius taught that people could resist or reject God's grace. He also taught that a person who was saved could lose his salvation. Both points are contrary to Calvin's teaching that God was so sovereign that His grace could not be resisted and that once a person was chosen for salvation, he cannot lose his salvation. Because of these points, most Calvinists have a knee-jerk reaction to any talking about free will that they must be Arminians.

Arminians are more readily described as semi-Calvinists. They are not the complete opposite. Arminians believe that no person can begin the process of being saved without the intervention of God.

John Wesley, for the most part, ascribed to Arminius' teachings. He did refine it. He also added the idea that people can mature and obtain perfect holiness. Thus, the religions that follow Wesley's teachings, such as the Methodists, the Church of the Nazarene, and most Pentecostal churches, are Arminian in nature. Religions that stick closer to Arminius' original teachings (without the holiness additions) are the Free Will Baptists and the American Baptists.