The doctrine of Predestination holds that before the creation of the universe, before time itself began, God Almighty determined who would go to ‘heaven' and who would go to ‘hell', not by works, as the Books of Romans insists, but simply by divine fiat, so that nothing at all would depend on human effort or human choices or human will, but only on the choice and work of God. As Paul insists, before either Jacob or Esau was born, and had done anything, either good or evil, God chose Jacob and condemned Esau. If you actually go back to the story of Genesis, and read the tale of Jacob and Esau, you can see that Paul's condemnation of Esau is something he obviously read into the original story, since Esau is more than simply evil incarnate in Genesis, has good reason to be angry at Jacob, who is a thief and a cheat.
The doctrine of Predestination is found in Romans and in Ephesians. It can be contrasted with the works based doctrine of salvation in a works based document like the gospel of Matthew. In this Gospel you are only saved if you get all your works done, if you don't get your works done, you get tortured or even executed, and only those who doggedly persist to the bitter end, and complete their assigned works will be saved. You are saved by works then, and this has led those who hold to Predestination and divine fiat to struggle with doctrines about ‘perseverance of the Saints' and other such things those who believe in pure 100% Predestination don't need to bother with.
Now Christian theology has often been a composite composed of bits of pieces from various traditions, and the differences in opinion about these divergent traditions in the Bible is what is responsible for what are known as ‘denominations' in the church.
Salvation is based on works in the church (the most important work you will ever do, the work of choosing to be saved). This is very obvious. This will lead ‘works based' Christians to attempt to integrate the opposing doctrine of Divine Fiat (Jacob did not do good, and thus get chosen, but rather the Doctrine of Divine Fiat is demonstrated in God's choosing Jacob the cheat over Esau, for example, simply so that it would be based on God's choice, and not any work or act of human choice or human effort and will, a doctrine the exact opposite of the works based approach to individual choice, effort, and will to do that one important church work required to ‘get saved'.) According to work's based churches God was able to look ahead and see that Jacob would get saved and Esau would go to hell, and thus based on the works of salvation that God knew ahead of time that Jacob would do, God predestined Jacob to salvation. This introduces some ‘justice' that was absent in that doctrine of pure predestination, where Paul casually announces that, by divine fiat, certain creatures had been deliberately created evil by God so that they could be destroyed in a display of divine anger for that same sinful wickedness, a doctrine so unjust, cruel and manipulative that Paul cannot justify it, but instead tells the critic to shut up and quit talking back and then resorts to terror and bullying. Not much of an answer, and the works based Matthew type churches know this as well, which is why they have watered down and misrepresented the doctrine of Predestination by introducing works and something they call ‘divine foreknowledge' to explain it all.
Now as a philosophy, made as it is of scraps from opposing traditions, the works based approach is a failure and if you wish to believe in the Omnipotence of God, and thus make God responsible for the creation of evil, then you really must become a Calvinist and believe in pure Predestination, because as a philosophy this is the only logical choice (the doctrine of Predestination is actually the inevitable and only logical conclusion to come to if you believe in the Perfect Flawless Omnipotence of God.) If God makes mistakes, then the doctrine of Predestination, and all its injustice become non-issues, and such things would only be an issue for those people with high theological concepts, who then must struggle with the existence of evil in the world, evil which could only have come from God. Now these same people with the Highest Loftiest Theology will also have to state that God is Good, that God is Just and Kind and all the other wonderful qualities required if some God is to be absolute perfection, and given the injustice, abuse of power relationships, and the simple cruelty of the doctrine of Divine Fiat (given that a God can never burn in hell), what must be done here is reconcile all this offensive cruel conduct with the other notions of Perfect Kind Goodness and Justice, and this can never be the case. It is this impossible nut that Christian Apologetics must attempt to crack, which is the best indictment I know of against the doctrine of Perfect Omnipotence and the logically following doctrine of Predestination. You see, my God is not the source of evil and all the cruel sufferings of the world, and none of this happened by Divine Design or simply by Divine Fiat. You see my God makes mistakes, and I accept that, and I don't find myself working on the useless task of cracking impossible nuts (an impossible task, by definition, which should tell you something right there...)
Nevertheless, for those who consider impossible nuts to be ‘a divine mystery' and believe that cracking such a nut is the task assigned by God, for them the doctrine of pure, pure non-works based Predestination is the only intellectually satisfying position to hold. You see, that works based thing about ‘knowing ahead of time' is in no important way dissimilar to the doctrine of Divine Fiat.
Now first let us assume, that, pure Predestination style, some Omnipotent being, simply by Divine Fiat, creates both good and evil, the condemned created condemned and the saved created to be saved, simply by Divine Fiat, and knows ahead of time the starvation and suffering of say, starved babies (hunger, like burning in hell forever, another thing never experienced personally by a God), but never mind. That Almighty and All Knowing All Powerful God will do all those things, and you should just shut your mouth about it, because, after all it is Perfect Omnipotent God.
Now let us assume that we adopt the watered down works based approach. Instead of saying, Predestination style, that works and human choices don't matter, we will insist that they do matter, and that the All Knowing eye of God simply noted those works ahead of time, Predestinating people to heaven or hell that way. There is a very subtle distinction being made here, in defense of the doctrine of Perfect Omnipotence, also favored by those works based churches. You see, having seen all that coming suffering, and having seen that burning in hell, as a God, a Perfect Omnipotent God with all the choices in the Universe, I could choose to take a few sensible steps ahead of time to avert disaster. This is the one benefit of knowing the future. It doesn't have to be that way. So you can see, that even that ‘saw their works ahead of time' argument is intellectually bankrupt, because you wind up back again where you started, with every thing being Predestined by Perfect Omnipotent God. Now if it were to depend on human choices and human effort and will as the works based gospel of Matthew insists, this becomes irrelevant when you consider how things have been deliberately created in such a way as to have that damnation scenario work out as it did, in any case, instead of being fixed, as it should have been fixed and avoided by any Omnipotent God who knew the future, if it turned out that such a God was worth a plug nickel (I certainly would have taken the steps required to avoid the situation in the first place, and it is highly unlikely that I am holier than a Perfect God).
As I said it is a particularly subtle distinction those works based churches try to make to integrate the opposing tradition of Predestination into their works based theology, and it is a bankrupt position in Philosophy because you just wind up back where you started in the end. The real solution for so many of those impossible nuts is to realize that this is an accident, Yahweh didn't plan it, and as for ‘divine mystery' well, who knows what really did happen, and what went wrong (certainly no one here knows a things about it).