In your example--"That world of misery, that lake of burning brimstone"--Edwards, one of the best preachers in the Calvinist church, yokes an abstract concept to a concrete image. In this case, "that lake of burning brimstone" is in apposition to "that world of misery," but appositives as such do not move people to fear. Edwards’ ability to turn the abstract “world of misery” into the frightening concrete image of “that lake of burning brimstone” helps him achieve his over-arching goal in this sermon to awaken his congregation’s religious devotion by reminding them of their danger from a wrathful God. His listeners might not respond to words like punishment, suffering, and Hell, but they will be truly shaken by Hell described as “the bottomless gulf” or “the wrath of God” as a flood ready to overwhelm them—again, the tension in this sermon is between an abstract concept and a concrete, everyday image that resonates with his frightened listeners.
Edwards’ rhetorical technique in this sermon is actually not characterized by the use of appositives, and if you look at your example, you will see that the operative clause--"that lake of burning brimstone"--is an easily visualized concrete image that makes real the abstraction of "that world of misery." With very few exceptions, Edwards creates fear in his listeners with metaphors and similes in which an abstract concept like being held over hell is likened to God or a person holding a spider over a fire, an image every listener can understand:
The God that holds you over the pit of hell, much as one holds a spider, or some loathsome insect over the fire, abhors you, and is dreadfully provoked: his wrath towards you burns like fire; he looks upon you as worthy of nothing else, but to be cast into the fire; he is of purer eyes than to bear to have you in his sight; you are ten thousand times more abominable in his eyes, than the most hateful venomous serpent is in ours.
What makes an appositive an appositive is its structure, so there is nothing particularly effective about the structure itself. What is effective is that the appositive in your example is metaphor, a specific, concrete, frightening image designed to remind Edwards' congregation that their danger is real. One a statistical basis, however, Edwards uses very few appositive structures and instead employs metaphorical language, without appositives, to create the sermon's atmosphere of immediate danger to his listeners
The appositive is used as a way to re-describe the subject of the sentence. Edwards uses the appositive to re-describe another aspect of the inferno to bring out its true horror to his audience. For example, "the world of misery" is one in which there is a lack of connection to the divine. Edwards describes this form of being as one in which God's wrath is invoked because of an absence of spiritual identity. This is the "world of misery" that Edwards re-describes as "that lake of burning brimstone." The purpose in re-describing it using the appositive phrase is to make this image more vivid in the audience's mind. Linking "that world of misery" with "that lake of burning brimstone" is a way for the audience to see the consequences of not taking the divine into their lives.
The appositive clause helps to illuminate the intent of the author. Edwards uses this technique at different points in his sermon. One such example is in the exposition. Edwards employs an appositive in describing the Israelites: "In this verse is threatened the vengeance of God on the wicked unbelieving Israelites, who were God's visible people..." The Israelites as described as "God's visible people" helps to illuminate another aspect of the Israelites' condition. Edwards uses the appositive later in the sermon as he is describing the word of the divine: " They do not only justly deserve to be cast down thither, but the sentence of the law of God, that eternal and immutable rule of righteousness that God has fixed between him and mankind..." Edwards is able to further develop how he sees the "law of God" by linking it with "eternal and immutable law of righteousness." This is another example where the appositive is used in the sermon.