"But what does this have to do with free will, foreknowledge, predestination, etc?"Calvinism teaches that God predestines some to eternal life based on no merit in them but merely out of grace. Calvinism further teaces that the elect believe as a result of God's producing new life in them. They are regenerated and believe. Arminianism taches that God predestines to eternal life those He foresees will respond to the gospel in faith. They believe and are regenerated.
Much of the debate centers, perhaps inadvertently, upon a fallacious conception of causation as being only aligned with the time dimension we mortals know. That conception forces us into the ridiculous dichotomy of the no-control-of-history God vs. a frozen chosen who don't worry about witnessing.
Hugh Ross has done some interesting analysis about what "might" (of course we cannot know exactly) be happening behind the scenes of our universe with a God who has invoked multiple time (causation) dimensions. It is an existence proof of the possibility of a creation which comes down (as we see it) in Calvinist terms without violating the tenets of Scripture and without vitiating man's power to choose without being forced by God.