Unconditional Election
Unconditional election is the belief that God chooses whom to elect to salvation independent of any choice or quality of those people. This is largely intertwined with total depravity—people are all naturally sinful and unable to choose God, so God must choose them on His own.
Ephesians 1:4–5 According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love: having predestinated us unto the adoption of children by Jesus Christ to himself, according to the good pleasure of his will,
More than just stating God chooses whom to save, it is clear that He chooses for His own reasons, unknown to us. There are no requirements we must do first. There is nothing we can do to earn His merit or to deserve salvation more than any other. From a human perspective, it is essentially random who goes to heaven and who goes to hell. We are all completely unworthy. Those whom He chooses to save deserve hell just as much as those already there. It is only by His gift of grace that any can be saved, and who is to say whom he gives it to?
The opposing view is conditional election. Where unconditional election says God chooses some to save ahead of time with no prior involvement by those saved, conditional election says God offers His grace to all but only elects people to be saved who choose to accept His grace.