In Christian theology there are two truths one major one minor. The sovereignity of God and the free will of man.
Now, much of these debates center around does sovereignity equal pre-determination. So if God is all knowing, all powerful, and all sovereign, does (or can) anything actually occur without being a function of his allowing it? The answer is no.
So if nothing can occur without it being allowed by God, then everything that does occur is allowed by God. Meaning that evil is allowed, sin, etc. If it is allowed, is it not sanctioned? If you have the power to stop something and you don't, even though you don't want that thing to exist, do you not sanction it? If you create all things, and something is evil, did you not create evil or the conditions by which evil can occur?
If indeed God created all things, then that must include the capacity for evil. Evil defined, IE harmatia (OT sin) simply means missing the mark. So sin, evil, etc. is simply a matter of missing Gods perfection. So if the scripture states the WE ALL sin, and fall short of the glory of God and it also states that we don't simply perform acts of sin, but are in a state of sin then how do we eliminate that state of sin, so we can meet God's perfect standard?
In both Armenianism and Calvinism, the elimination of the state of sin is salvation through Jesus Christ.
So we have determined that God allows evil to occur, and that men are evil (in the sense that they miss the mark of perfection), and therefore need salvation.
This is where it gets tricky.
Armenians believe in free will, Calvinist believe in limited free will or in predestination.
Armenians believe that all men have the capacity to choose salvation. Calvinist believe in "irresistable grace" meaning that you have no choice, if you are one of Gods elect, you will be saved.
So lets put it all together. If God created the capacity for evil, which befalls all men, and he has an 'elect' which is predetermined, the doesn't this also mean that God predetermined men to hell? Maybe.
Some say that predestination is a result of foreknowledge, meaning that God already knew who would use their free will to 'choose' and therefore he predestined them. Others who are pure Calvinist say he straight up chose, and it has nothing to do with freewill.
Armenians on the other hand believe that men MUST choose Christ, and that God does not predetermine them for salvation. God may know who will get saved, but it is solely the work of the man choosing Christ. When confronted with the question of "what if someone doesn't hear about Jesus" there answer is, if he / she is a 'true' seeker, Christ will be revealed.
So that is it in a nutshell.
Calvinist believe all men are sinful, and that God has chosen his elect, either due to direct choice, or foreknowledge of who will be chosen, but that there is always a predetermined amount of folks who will be saved.
Armenians believe that all men have the ability to be saved, and can choose to be saved, because all men have freewill and choice.