The last point of Calvinism is the Perseverance of the Saints. It teaches that God has drawn the elect to salvation and that God draws them to continue to believe. The elect cannot totally fall away from grace, and if they do backslide into sin, it is temporary and God will restore them, causing them to persevere in faith and in salvation.
Armianism teaches the Conditional Preservation of the Saints. It teaches that as long as the individual has persevering faith in Jesus, then the condition is satisfied and they will be saved. They take the warnings seriously in scripture that people can lose their faith and miss out on salvation. So they encourage believers to continue to walk in faith.
When all the pieces are put together ...
People are so sinful they can never choose not to be and would resist all offers for salvation. Before people even existed, God chose the elect - a group of people whom He would save not because of anything they did or would do. In his sovereignty, God simply chose them - elected them for salvation and eternal life. Jesus atonement was made specifically for them, and His irresistible grace would see to it that they would accept the offer for salvation. Then God would see to it that they would continue to believe in Him. Everyone else - the not-elect will remain in sin, will refuse the offers of salvation, and will choose not to believe in Jesus because they do not have free will to do otherwise and wouldn't have chosen salvation if it was offered to them anyway.
People are pretty sinful, but God sends a special kind of grace that enables people to chose to be saved. God didn't just chose the elect to be saved, but he foresaw everyone who would believe in Jesus out of their own free will and predestined them to choose salvation. Jesus atonement is sufficient for all of them if they simply believe in Him. Everyone else who do not choose salvation made the choice out of their own free will and had every opportunity to choose salvation. As long as they live, they can still choose to believe. As long as they choose to believe, their salvation is secure.
I'm just really glad that the Scriptures say nothing about a pop quiz about having the right beliefs in order to be saved. But it scares me that too many Christians have made it a litmus test of true belief that we have the correct knowledge of Scripture. Another name for Calvinism is the Doctrines of Grace but after reading up about it - I'm not so sure the name isn't a misnomer.
Calvinism says that God's grace is for the elect. God chose the elect before he created the world or anyone in it. God's grace draws the elect to salvation. The elect cannot resist God's grace, so it causes them to be saved. It causes them to continue in their belief. The elect will go to heaven where they will praise God for eternity. God's grace would have been enough to save the whole world, if it were his plan, but it's not. Everyone else is not elect. They are resistant to God's irresistible grace. They wouldn't and couldn't choose to believe in Jesus because their wills are corrupted by sin. When they die, they will die in sin, without salvation and without God's grace, they will be judged and go hell where they will spend eternity being punished.
Arminianism says that predestined those he foreknew would chose to believe in him of their own free will. The offer of salvation is meant for everyone and God's grace has opened the door for everyone to be saved. All believers have to do is to continue to believe. As Roger Olsen puts it, they have 'freed will' - sin doesn't condemn humanity to be defaulted to unable to respond to grace, God's grace gives everybody a choice whether or not to accept the free gift of salvation. Once they have accepted the gift, they can choose to continue to walk in faith or they can chose to walk away.
These days, Calvinism has a huge following - it even has a lot of people preaching it as if it were the only Biblical doctrine of grace that all real, true, believers must accept to prove that their salvation is secure. It's extremely important to have the correct biblical knowledge - but it's also not really what Jesus was getting to in the core of his ministry. Look at the Sermon on the Mount - Jesus was trying to get believers that it's not what you believe that matters, but how you act on what you believe. It's not enough to be a Priest or Levite who is pure, but it is enough to be a half-blooded heretic who displays mercy and compassion. It's not enough to excel at tithing even a tenth of spices, it is enough to tithe justice, mercy, and faithfulness.
Calvinism says that we can't really know who the elect are, but that because faith and works go hand-in-hand, works are proof of one's saving faith. I remember watching a documentary that said as much - about how many believers in calvinism also lived out the 'protestant work ethic' in every sense of the word. I wondered - what do they do with the evidence that there are people the world over who do good works, give to charity, volunteer their time, raise money for important causes - who don't profess to believe in Calvinism? (Does that mean Calvinism itself is not the true test of one's genuine belief? That people can be saved apart from belief in Calvinism? or who aren't even Christian? If all good works are egoist and selfish, then how does one tell the difference between a not-elect person who does good deeds and an elect person who does the very same good deeds? Can the elect do good works and also be egoist and selfish as he or she goes about them?
Arminianism allows for God's grace to make away for anyone who believes to be saved - it didn't decide millennia ago who would be saved. It gives hope to the hopeless and that's why I like it better - but I've come to realize that I don't really believe in either of them fully. I get that people sin, but I don't really care about the Original Sin, Satan falling from Heaven, or the history of events that occurred in eternity past, long before creation. I get that people are sinners, but I don't think we're default to "living in sin, unable to respond to grace." I think we do have free wills and God wants the whole world of people with free will to choose what we believe, if we want to believe in him, and to continue to choose to believe even when times get difficult.
This doesn't really do anything to resolve my current crisis of belief - if Calvinism is true, then I'm not really going through a crisis because God will see to that I will believe if I'm elect, but a lack of works might prove that I'm not elect and then I can't really believe in Him at all. If Arminianism is true, then I'm in danger - it's not a comforting message. In this world, continued belief in something is difficult. Kids can be taught to believe in Santa and the Easter Bunny, but by the time they are adults they are expected to be in disbelief. We can believe in our pastors and teachers, but they're sinning sinners who can lose even the stoutest believer in them when they do something they shouldn't. We can lose faith in our sports idols as they break the rules. We can lose faith in the direction our leaders are heading when they get us into trouble. So it shouldn't come as a surprise that faith has it's highs and it's lows. Maybe there's a bright side though, maybe it's not Arminianism or Calvinism that died or was resurrected or promises salvation - I don't have to believe in either one but in the one they both point to. And that's good enough for me for now.