This is the notion that some people are saved and others are not; all according to God’s choice. God elected, or chose, those who would spend eternity with Him. The nature of election is widely debated however.
Calvinists claim that man is unconditionally elected not based on any merit. Arminians claim that God foreknew those who would follow Him and then chose according to that knowledge.
There are others who believe that references to election in the Bible are not concerning individuals at all. Letters of the New Testament addressed to “the elect” are not addressed to individuals but rather the church as a whole. God elected the church for salvation in eternity past and did not determine each and every individual who would be saved. When they are saved, they become part of the elect.
Arminianism is named for its founder Jacobus Arminius. It is a response to the beliefs of John Calvin. Arminius was a follower of Calvin until he was challenged to a debate to defend his views and found his opponent more able to defend his views.
Central to Arminian belief is that man has free will and is capable choosing to follow God. This is contrary to the teachings of Calvin and Martin Luther who both taught that man’s will was surrendered at the Fall.
In 1610 Arminius and his followers issued the Remonstrance, five points countering the beliefs of of Calvinism. The Synod of Dort would later in 1619 issue the five points of Calvinism in response to the Remonstrance.
Calvin stressed man’s inability to reach out to God while Arminius believed that God opened the door for man to make the decision. Opponents of Arminianism believe that it is the direct opposite of Calvinism and states that man is fully able to save himself. This is not the case but the view has been adopted by some who have been labeled as Arminians because they do not hold a Calvinistic view.
The Five Points of Arminianism:
Election based on foreknowledge
For more information, see the articles Arminianism Basics and Arminianism vs. Calvinism.