John Calvin is mostly strongly associated with the doctrine of predestination. This theology maintains that an individual can be saved only by God. God has predestined or pre-ordained that certain people will go to heaven. This is based not on what they do or how they respond to God's call, but solely on God's will. However, even a person chosen by God can, through their own sin, negate that predestined fate and end up in hell. This is a controversial theology based in rejecting the Roman Catholic theology that a person can earn their way to heaven through good works.
Another theological position associated with Calvin is total depravity. This is the idea that every human is born with the capacity for sin; we all will sin or do something outside of God's will, no matter how good we are, because we live in a fallen world that confuses us about the nature of good and evil. However, humans are made in the image of God, so Calvin maintained that no human, no matter how bad, was utterly depraved. Even Adolph Hitler, Calvin would argue (were he alive to witness Hitler), was not utterly depraved: he probably, at one point in his life, did one good act for one person, such as perhaps helping an old lady cross the street.
Calvin also rejected the real presence aspect of the eucharist and understood communion as a celebration commemorating Christ's sacrifice. If the Roman Catholics emphasized Christ's words, "this is my body and blood," Calvin focused on Christ saying "do this in remembrance of me." This may seem small to us now, but at the time, it was a radical position over which much blood was shed.
Calvin's theology can seem harsh, but what he wants to emphasize is the total human dependence on God. If we realize that we owe God for everything, Calvin thought, we are less likely to be arrogant and unkind and more likely to be grateful and generous. At the same time, Calvin's theology can be difficult for the modern person to warm up to.