In "Sinners in the Hands of an Angry God," what sin is being discussed?
The European Renaissance had taken hold and was beginning to infiltrate American thought when Jonathan Edwards delivered this sermon in 1741. Renaissance thought stressed the triumph of reason (which tends to negate the need for faith), where ""Man is the measure of all things" (a quote from Pythagoras).
After he finishes explaining the several reasons God can and will crush all sinners--with whom he is enraged--at any moment, he addresses why they will die and go to hell, unless they embrace Christ and beg for forgiveness.
The sin he points out is implied in paragraph 9, where he says that "almost every natural man that hears of hell, flatters himself that he shall escape it; he depends upon himself for his own security; he flatters himself in what he has done, in what he is now doing, or what he intends to do." That is, you just think that you can get into heaven by your own actions, just by being a good person, but you can't. This is the sin of pride.
Later, in his "Application" section, he adds that "the sun does not willingly shine upon you to give you light to serve sin and Satan; the earth does not willingly yield her increase to satisfy your lusts," suggesting that lust was also a matter of concern. However, the greater part of the sermon is clearly aimed at those who believe they can reach heaven without God's help (that is, God grace).