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Arminius distinguishes between legal theology and evangelical theology. Regarding, the latter, as sinners, because of the gracious estimation of God, faith is our righteousness. The righteousness of Christ is not imputed to believers, according to Arminius. He did not seem to believe Christ's righteousness could be imputed. Arminius made use of a concept, known as acceptilatio. Imperfect faith is accepted (by God's gracious estimation) as righteousness. Or, to put it another way, the human act of faith is by grace counted as evangelical righteousness, as if it were the complete fulfillment of the whole law. This genuine human act comes forth from the ability to choose (liberum arbitrium). God has a "new law" in the evangelical covenant, whereby faith answers to the demands of the covenant. Arminius clearly struggled in coming to a settled view....What is the problem? Because the act of faith constitutes righteousness, the manner in which a sinner is justified is not because of the righteousness of Christ imputed to us through the instrument of faith, but because of the act of believing which answers to the demands of the evangelical covenant....God considers our righteousness (i.e., act of faith) as something that it is not (i.e., perfect).

The Reformed, however, view imputation as secundum veritatem - God considers Christ's righteousness as our righteousness, precisely because it is, through union with Christ. The verdict that God passes on his Son is precisely the same verdict he passes on those who belong to Christ - but only through imputation. In other words, technically we can stand before the tribunal of God with as much assurance of our righteousness as Christ can before the Father. Not because God accepts imperfection, but because God demands perfection from all who would enter life, and we possess a perfect righteousness, by imputation. This is why justification cannot be revoked (i.e., we cannot lose our salvation). Justification by faith (in the Reformed schema) has important implications for our doctrine of perseverance.

This hint of subordinationism in Arminius' understanding of the mediatorial office of the Son is more pronounced in his claim that the Son receives His deity, and not merely His personality as Son, from the Father. For Arminius, the Son is not autotheos, but has both "divine essence" and "divine life" of himself. In part, his argument is that the Reformed view of the "autotheotic" reality of the three persons is inevitably tritheistic: "the Reformed doctrine of the Son's aseity . . . violates the unity of the divine essence by postulating three divine persons each God from himself -- in short, by postulating three separate deities and lapsing into tritheism". From his reading of the fathers, Arminius concluded that "God the Father [is] the principium of the Godhead"....
....In contrast to the Reformed theologians of his time, Arminius believed that the atonement was accomplished purely by the passive obedience of Christ. By his life, Jesus was qualified and prepared to exercise his priesthood, but He actually exercised that priesthood only in his death....Thus "rather than use the idea of a voluntary self-emptying to explain the way in which the eternal Son is subordinate to his work, Arminius tends to view the subordination in terms of the order of persons in the Trinity and to view Christ's as conferred by the Father, without reference to the will or act of the Son"....
....Because Christ's active obedience plays no role in Arminius' understanding of the atonement, room is opened up for human obedience as the means for accomplishing salvation: "As in the satisfaction-theory of the medieval doctors, the distinction between a salvific passive obedience of Christ and a non-salvific active obedience points in the theology of Arminius toward a doctrine of human involvement or cooperation in the work of salvation. In other words, Arminius' separation of Christ's active and passive obedience in his christological locus correlates with his soteriological synergism".
-- from the thread Arminius's Christology
A third view of the atonement was devised by Hugo Grotius (1583-1645) during the Arminian controversy in Holland. Known as the governmental theory of the atonement, this view is something of a middle road between Abelard and Anselm. According to Grotius, Christ’s death was a public display of God’s justice, but not an actual payment on behalf of sinners. In other words, the cross shows what punishment for sin would look like if God recompensed sin. But no actual vicarious payment of the sinner’s debt was made by Christ.
Grotius, like Abelard and the Socinians, believed God could forgive sin without any payment. But Grotius said the dignity and authority of God’s law still needed to be upheld. Sin is a challenge to God’s right to rule. If God simply overlooked sin, He would in effect abrogate His moral government of the universe. So Christ’s death was necessary to vindicate God’s authority as ruler, because it proved His willingness and his right to punish, even though He ultimately relinquishes the claims of His justice against repentant sinners. Christ’s death therefore was not a substitute for anyone else’s punishment, but merely a public example of God’s moral authority and His hatred of sin.
In other words, unlike Abelard, Grotius saw that the death of Christ displayed the wrath, as well as the love, of God. Like Abelard, however, Grotius believed the atonement was exemplary rather than substitutionary. Christ did not actually suffer in anyone’s place. The atonement accomplished nothing objective on the sinner’s behalf; it was merely a symbolic gesture. Christ’s death was an example only. And redemption therefore hinges completely on something the sinner must do.
-- excerpted from John MacArthur, Open Theism's Attack on the Atonement