Arminian doctrine is the term for a theological stance originating with James Arminius - a contemporary of John Calvin. His views include:
1). "Conditional Predestination" - which basically states that God predestines those He knows ahead of time will accept him; whereas Calvin taught an unconditional election;
2). "Free Will of Man" - a teaching that says that man is a free moral agent can actually choose God;
3). Unlimited Atonement - a teaching that Christ died for more than just the elect;
4). Resistible Grace - a teaching that says that since man is a free moral agent, if God calls him specifically to salvation, he can say no to God. and
5) - the most radical and troubling of all arminian doctrine: a teaching that you can lose your salvation, totally rejecting eternal security. They believe that you must live righteously if you are to retain your saved state. Through sin, a person who was once saved can lose it and be damned. This clearly violates the teachings of God's Word.
Calvinism on the other hand believes in five basic tenets forming the acronym "TULIP":
1) Total depravity - in man there dwells no good thing
2) Unconditional election - since man is totally depraved, election is not based on any merit whatsoever other than the eternal counsel of the will of God
3) Limited atonement - Christ died only for the elect
4) Irresistible grace - Every man who receives an "effectual call" by God's Spirit to salvation will be saved - you cannot refuse God.
5) Perseverance of the Saints - those saved by the power of God are eternally secure and will remain in a righteous condition because of it.
I trust these clarifications can be of assistance.